Move hexadecimal to radices page.

notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json

@@ -90,7 +90,7 @@
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@@ -107,7 +107,7 @@
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     "templates/daily.md": "7866014e730e85683155207a02e367d8",
-    "posix/regexp.md": "43825a1b9ed0dd7eeb1b6fe35c928bfe",
+    "posix/regexp.md": "f5fb177c7356faf1bf768023c2563c54",
     "journal/2024-02-04.md": "e2b5678fc53d7284b71ed6820c02b954",
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@@ -128,7 +128,7 @@
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     "algorithms/index 1.md": "6fada1f3d5d3af64687719eb465a5b97",
     "binary/hexadecimal.md": "c3d485f1fd869fe600334ecbef7d5d70",
-    "binary/index.md": "ab345e75dc01f890faa31bc26676d526",
+    "binary/index.md": "d97bddf94227df5903a2929febf25606",
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@@ -166,7 +166,7 @@
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     "_journal/2024-02/2024-02-15.md": "16cb7563d404cb543719b7bb5037aeed",
-    "algebra/floor-ceiling.md": "456fa31bedb9ec7c2fa1d6f75db81dec",
+    "algebra/floor-ceiling.md": "efc4502ed22128e14b20ba88b368a872",
     "algebra/index.md": "90b842eb694938d87c7c68779a5cacd1",
     "algorithms/binary-search.md": "08cb6dc2dfb204a665d8e8333def20ca",
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@@ -179,11 +179,14 @@
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-    "combinatorics/permutations.md": "9351e4d5c4457c34198640cf04bdd888",
+    "combinatorics/permutations.md": "606b4b2b8018797ca54857112235d96e",
-    "combinatorics/combinations.md": "2e7069e018525e10e4e2b9fb46bc8291",
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-    "combinatorics/inclusion-exclusion.md": "4d5ba716bc90cd378c7c4c816b224c75"
+    "combinatorics/inclusion-exclusion.md": "4d5ba716bc90cd378c7c4c816b224c75",
+    "_journal/2024-02-21.md": "d7545ab01e651e565c056ded99455286",
+    "_journal/2024-02/2024-02-20.md": "af2ef10727726200c4defe2eafc7d841",
+    "algebra/radices.md": "1171835a864103fbc4cbe21d56fcfa1f"
   },
   "fields_dict": {
     "Basic": [

notes/_journal/2024-02-21.md

@@ -0,0 +1,11 @@
+---
+title: "2024-02-21"
+---
+
+- [x] Anki Flashcards
+- [x] KoL
+- [ ] Sheet Music (10 min.)
+- [ ] OGS (1 Life & Death Problem)
+- [ ] Korean (Read 1 Story)
+- [ ] Interview Prep (1 Practice Problem)
+- [ ] Log Work Hours (Max 3 hours)

notes/algebra/floor-ceiling.md

@@ -21,7 +21,7 @@ END%%
 %%ANKI
 Basic
 What is the floor of $x$?
-Back: The greatest integer less than $x$.
+Back: The greatest integer less than or equal to $x$.
 Reference: Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik, *Concrete Mathematics: A Foundation for Computer Science*, 2nd ed (Reading, Mass: Addison-Wesley, 1994).
 <!--ID: 1708110779649-->
 END%%
@@ -37,7 +37,7 @@ END%%
 %%ANKI
 Basic
 What is the ceiling of $x$?
-Back: The least integer greater than $x$.
+Back: The least integer greater than or equal to $x$.
 Reference: Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik, *Concrete Mathematics: A Foundation for Computer Science*, 2nd ed (Reading, Mass: Addison-Wesley, 1994).
 <!--ID: 1708110779663-->
 END%%
@@ -68,7 +68,7 @@ END%%
 
 %%ANKI
 Basic
-What can be said about $x$ if $\lceil x \rceil - \lfloor x \rceil = 0$?
+What can be said about $x$ if $\lceil x \rceil - \lfloor x \rfloor = 0$?
 Back: $x$ is even.
 Reference: Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik, *Concrete Mathematics: A Foundation for Computer Science*, 2nd ed (Reading, Mass: Addison-Wesley, 1994).
 <!--ID: 1708110779687-->
@@ -76,7 +76,7 @@ END%%
 
 %%ANKI
 Basic
-What can be said about $x$ if $\lceil x \rceil - \lfloor x \rceil = 1$?
+What can be said about $x$ if $\lceil x \rceil - \lfloor x \rfloor = 1$?
 Back: $x$ is odd.
 Reference: Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik, *Concrete Mathematics: A Foundation for Computer Science*, 2nd ed (Reading, Mass: Addison-Wesley, 1994).
 <!--ID: 1708110779693-->
@@ -195,7 +195,7 @@ END%%
 %%ANKI
 Basic
 If `A[p..q]` has odd size, what `r` most fairly allows partitions `A[p..r]` and `A[r+1..q]`?
-Back: $r = \lfloor (p + q) / 2 \rfloor$
+Back: $r = \lfloor (p + q) / 2 \rfloor = \lceil (p + q) / 2 \rceil$
 Reference: Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik, *Concrete Mathematics: A Foundation for Computer Science*, 2nd ed (Reading, Mass: Addison-Wesley, 1994).
 <!--ID: 1708114757958-->
 END%%
@@ -203,7 +203,7 @@ END%%
 %%ANKI
 Basic
 If `A[p..q]` has odd size, what `r` most fairly allows partitions `A[p..r-1]` and `A[r..q]`?
-Back: $r = \lceil (p + q) / 2 \rceil$
+Back: $r = \lfloor (p + q) / 2 \rfloor = \lceil (p + q) / 2 \rceil$
 Reference: Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik, *Concrete Mathematics: A Foundation for Computer Science*, 2nd ed (Reading, Mass: Addison-Wesley, 1994).
 <!--ID: 1708114757961-->
 END%%

notes/algebra/radices.md

@@ -1,26 +1,108 @@
 ---
-title: Hexadecimal
+title: Radices
 TARGET DECK: Obsidian::STEM
-FILE TAGS: binary::hex
+FILE TAGS: algebra
 tags:
-  - binary
+  - algebra
-  - hexadecimal
 ---
 
 ## Overview
 
-Hexadecimal encoding refers to the 16-base representation of binary numbers. Distinguish potentially ambiguous values like $32$ with the base as a subscript, e.g. $32_{10}$ vs $32_{16}$.
+The **radix** is the number of unique digits used to represent numbers in a positional numeral system. Most commonly used systems tend to be binary ($2$-base), octal ($8$-base), decimal ($10$-base), and [[#Hexadecimal|hexadecimal]] ($16$-base).
+
+%%ANKI
+Basic
+What is the process of subtracting a larger digit from a smaller one in radix $r$?
+Back: Decrement the next non-zero and add $r$ to the smaller digit in question.
+Reference: “Radix,” in *Wikipedia*, August 6, 2023, [https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173](https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173).
+<!--ID: 1708534662981-->
+END%%
+
+%%ANKI
+Basic
+What does the first step in the subtraction process of $100_2 - 10_2$ *look* like?
+Back: $020_2 - 10_2$
+Reference: “Radix,” in *Wikipedia*, August 6, 2023, [https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173](https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173).
+<!--ID: 1708534662989-->
+END%%
+
+%%ANKI
+Basic
+In a positional numeral system, what does "radix" refer to?
+Back: The number of unique digits used to represent numbers.
+Reference: “Radix,” in *Wikipedia*, August 6, 2023, [https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173](https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173).
+<!--ID: 1708534662993-->
+END%%
+
+%%ANKI
+Basic
+What is the radix of the decimal system?
+Back: $10$
+Reference: “Radix,” in *Wikipedia*, August 6, 2023, [https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173](https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173).
+<!--ID: 1708534662997-->
+END%%
+
+%%ANKI
+Basic
+What is the radix of the octal system?
+Back: $8$
+Reference: “Radix,” in *Wikipedia*, August 6, 2023, [https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173](https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173).
+Tags: binary
+<!--ID: 1708534663001-->
+END%%
+
+%%ANKI
+Basic
+What is the radix of the hexadecimal system?
+Back: $16$
+Reference: “Radix,” in *Wikipedia*, August 6, 2023, [https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173](https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173).
+Tags: binary::hex
+<!--ID: 1708534663005-->
+END%%
+
+%%ANKI
+Basic
+What is the radix of the binary system?
+Back: $2$
+Reference: “Radix,” in *Wikipedia*, August 6, 2023, [https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173](https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173).
+Tags: binary
+<!--ID: 1708534663009-->
+END%%
+
+## Hexadecimal
+
+Hexadecimal is a 16-base numeral system, usually represented with digits `0` to `9` and `a` to `f` or `A` to `F`.
+
+%%ANKI
+Cloze
+A hexadecimal digit represents {4} bits.
+Reference: “Radix,” in *Wikipedia*, August 6, 2023, [https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173](https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173).
+Tags: binary::hex
+<!--ID: 1708534663013-->
+END%%
+
+%%ANKI
+Cloze
+An octal digit represents {3} bits.
+Reference: “Radix,” in *Wikipedia*, August 6, 2023, [https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173](https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173).
+Tags: binary
+<!--ID: 1708534663018-->
+END%%
 
 %%ANKI
 Cloze
 A byte consists of {2} hexadecimal digits.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
 <!--ID: 1707432641563-->
 END%%
 
 %%ANKI
+Cloze
 A nibble consists of {1} hexadecimal digits.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
+<!--ID: 1708534663022-->
 END%%
 
 %%ANKI
@@ -28,6 +110,7 @@ Basic
 Hexadecimal digits are represented by what characters?
 Back: `a` to `f`, `A` to `F`, and `0` to `9`.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
 <!--ID: 1707432641565-->
 END%%
 
@@ -36,6 +119,7 @@ Basic
 How does C denote a hexadecimal numeric constant?
 Back: With `0x` or `0X`.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex c
 <!--ID: 1707432641567-->
 END%%
 
@@ -44,6 +128,7 @@ Basic
 What is the decimal equivalent of hex `A`, `C`, and `F`?
 Back: `10`, `12`, and `15` respectively.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
 <!--ID: 1707432641568-->
 END%%
 
@@ -52,6 +137,7 @@ Basic
 What is the hexadecimal equivalent of decimal `11`, `12`, and `14`?
 Back: `B`, `C`, and `E` respectively.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
 <!--ID: 1707432641570-->
 END%%
 
@@ -60,6 +146,7 @@ Basic
 *When* should padding be introduced in binary to hexadecimal conversion?
 Back: When the number of bits is not a multiple of `4`.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
 <!--ID: 1707432641571-->
 END%%
 
@@ -68,6 +155,7 @@ Basic
 *Where* is padding introduced in binary to hexadecimal conversion?
 Back: To the left of the binary sequence.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
 <!--ID: 1707432641573-->
 END%%
 
@@ -76,6 +164,7 @@ Basic
 What are the possible hex values the first digit of $2^n$ can take on?
 Back: `1`, `2`, `4`, and `8`.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
 <!--ID: 1707432641579-->
 END%%
 
@@ -84,6 +173,7 @@ Basic
 What are the possible values in binary that the first nibble of $2^n$ can take on?
 Back: `0001`, `0010`, `0100`, and `1000`.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
 <!--ID: 1707432641580-->
 END%%
 
@@ -92,6 +182,7 @@ Basic
 How is $j$ interpreted in the hex representation of $2^{i + 4j}$?
 Back: As the number of `0`s in the encoding.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
 <!--ID: 1707432641582-->
 END%%
 
@@ -100,6 +191,7 @@ Basic
 How is the $0$ in $2^{0 + 4j}$ translated to hex?
 Back: As hex digit `1`.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
 <!--ID: 1707432641583-->
 END%%
 
@@ -108,6 +200,7 @@ Basic
 How is the $1$ in $2^{1 + 4j}$ translated to hex?
 Back: As hex digit `2`.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
 <!--ID: 1707432641585-->
 END%%
 
@@ -116,6 +209,7 @@ Basic
 How is the $2$ (power) in $2^{2 + 4j}$ translated to hex?
 Back: As hex digit `4`.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
 <!--ID: 1707432641586-->
 END%%
 
@@ -124,6 +218,7 @@ Basic
 How is the $3$ in $2^{3 + 4j}$ translated to hex?
 Back: As hex digit `8`.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
 <!--ID: 1707432641587-->
 END%%
 
@@ -132,6 +227,7 @@ Basic
 How is $n$ in $2^n$ factored to quickly write the decimal value's hex representation?
 Back: $n = i + 4j$ where $0 \leq i \leq 3$.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
 <!--ID: 1707432641589-->
 END%%
 
@@ -140,6 +236,7 @@ Basic
 How is the *remainder* of e.g. `158 / 16` managed in decimal to hex conversion?
 Back: As the next least significant bit of our conversion.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
 <!--ID: 1707432641594-->
 END%%
 
@@ -148,6 +245,7 @@ Basic
 How is the *quotient* of e.g. `158 / 16` managed in decimal to hex conversion?
 Back: As the next value to divide by `16`.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
 <!--ID: 1707432641595-->
 END%%
 
@@ -156,6 +254,7 @@ Basic
 When does repeated division in decimal to hex conversion end?
 Back: When the quotient (*not* the remainder) is `0`.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
 <!--ID: 1707919792632-->
 END%%
 
@@ -164,9 +263,11 @@ Basic
 How is e.g. `0xAC32` expressed as a sum of decimal values?
 Back: $(16^3 \times 10) + (16^2 \times 12) + (16^1 \times 3) + (16^0 \times 2)$
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
 <!--ID: 1707432641596-->
 END%%
 
 ## References
 
 * Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+* “Radix,” in *Wikipedia*, August 6, 2023, [https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173](https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173).

notes/binary/index.md

@@ -8,7 +8,7 @@ tags:
 
 ## Overview
 
-A binary digit or **bit** is a `0` or `1` character. A **bit string** is then a contiguous sequence of bits. It's **weight** is a reference to the number of `1`s in the bit string. Compare the below operation to the method for converting from one numerical base to another (e.g. [[hexadecimal]]).
+A binary digit or **bit** is a `0` or `1` character. A **bit string** is then a contiguous sequence of bits. It's **weight** is a reference to the number of `1`s in the bit string. Compare the below operation to the method for converting from one numerical base to another (e.g. [[radices#Hexadecimal|hexadecimal]]).
 
 ```c
 unsigned int bit_weight(int64_t n) {

notes/c/escape-sequences.md

@@ -49,7 +49,7 @@ Tags: bash
 <!--ID: 1706975891817-->
 END%%
 
-* `\xhh`: Consists of one or more hexadecimal digits. The `x` prefix is required to distinguish from octal escape sequences.
+* `\xhh`: Consists of one or more [[radices#Hexadecimal|hexadecimal]] digits. The `x` prefix is required to distinguish from octal escape sequences.
 	* [[bash/index|Bash]] supports this sequence as `$'\xhh'`. One or two digits is supported.
 	* [[gawk/index|gawk]] limits processing to two digits.
 		* Robbins states that using more than two hexadecimal digits can produce undefined results.

notes/combinatorics/combinations.md

@@ -90,12 +90,20 @@ END%%
 
 %%ANKI
 Basic
-How is the closed formula of $\binom{n}{k}$ written in terms of factorials (*not* falling factorials)?
+Without using falling factorials, what is the closed formula of $\binom{n}{k}$?
 Back: $$\binom{n}{k} = \frac{n!}{k!(n - k)!}$$
 Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
 <!--ID: 1708368078700-->
 END%%
 
+%%ANKI
+Basic
+Using falling factorials, what is the closed formula of $\binom{n}{k}$?
+Back: $$\binom{n}{k} = \frac{(n)_k}{k!}$$
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708532069694-->
+END%%
+
 %%ANKI
 Basic
 How do $k$-permutations of $n$ objects relate to $k$-combinations?
@@ -354,6 +362,68 @@ Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n
 <!--ID: 1708434662166-->
 END%%
 
+### Stars and Bars
+
+The **stars and bars** chart refers to a graphical depiction of distributing $n$ objects (represented as $*$) into $m$ different buckets (delineated via $|$. An example chart looks like so: $$**|***|*||*$$
+
+Notice there are $m - 1$ bars and interspersed amongst the $n$ stars. In the above example, there are $11$ total symbols, $4$ of which are bars, meaning there are $\binom{11}{4}$ ways to distribute the objects amongst the $5$ buckets. We can represent this using bit strings instead, with `0`s as stars and `1`s as bars. The above example is equivalently written as: $$00100010110$$
+
+%%ANKI
+Basic
+What symbols are typically used in a stars and bars chart?
+Back: $*$ and $|$
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708532069700-->
+END%%
+
+%%ANKI
+Basic
+What property is exhibited by objects distributed in a stars and bars chart?
+Back: They are identical to one another.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708532069704-->
+END%%
+
+%%ANKI
+Basic
+What kind of chart is the following an example of? $$**|***|*||*$$
+Back: Stars and bars
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708532069707-->
+END%%
+
+%%ANKI
+Basic
+How is the following stars and bars chart written as a bit string? $$**|***|*||*$$
+Back: $00100010110$
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708532069711-->
+END%%
+
+%%ANKI
+Basic
+The following stars and bars chart is a single instance of how many possible choices? $$**|***|*||*$$
+Back: $\binom{11}{4}$
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708532069714-->
+END%%
+
+%%ANKI
+Basic
+What graphical depiction is used to find the number of integer solutions to the following equation? $$x_1 + x_2 + \cdots + x_k = n$$
+Back: Stars and bars
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708532069717-->
+END%%
+
+%%ANKI
+Basic
+What *is* the distribution corresponding to the following stars and bars chart? $$*||*$$
+Back: A single object in the first and last bucket. No object in the middle.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708532069719-->
+END%%
+
 ## Lattice Paths
 
 A **lattice path** is one of the shorted possible paths connecting two points on a lattice, moving only horizontally and vertically. By representing each horizontal move by `1` and each vertical move by `1`, we see every lattice path has a corresponding [[#Bit Strings|bit string]].

notes/combinatorics/permutations.md

@@ -188,7 +188,7 @@ END%%
 
 %%ANKI
 Basic
-What is the closed formula for $(n)_k$ (falling factorial)?
+What is the closed formula for falling factorial $(n)_k$?
 Back: $$(n)_k = \frac{n!}{(n - k)!}$$
 Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
 <!--ID: 1708366788619-->

notes/posix/regexp.md

@@ -294,7 +294,7 @@ Class        | Similar To      | Meaning
 `[:punct:]`  |                 | All graphic characters except letters and digits
 `[:space:]`  | `[ \t\n\r\f\v]` | Whitespace characters
 `[:upper:]`  | `[A-Z]`         | Uppercase alphabetic characters
-`[:xdigit:]` | `[0-9A-Fa-f]`   | Hexadecimal digits
+`[:xdigit:]` | `[0-9A-Fa-f]`   | [[radices#Hexadecimal\|Hexadecimal]] digits
 
 %%ANKI
 Basic