diff --git a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json index b55222a..3d112cd 100644 --- a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json +++ b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json @@ -83,7 +83,12 @@ "merge-sort.gif", "theta-notation.png", "big-o-notation.png", - "big-omega-notation.png" + "big-omega-notation.png", + "ordering-y-repetition-y.jpg", + "ordering-repetition.jpg", + "ordering-y-repetition-n.jpg", + "ordering-n-repetition-y.jpg", + "ordering-n-repetition-n.jpg" ], "File Hashes": { "algorithms/index.md": "cd7c7ba91fb2f961c9f2437777e8e2ac", @@ -176,7 +181,7 @@ "_journal/2024-02-17.md": "7c37cb10515ed3d2f5388eaf02a67048", "_journal/2024-02/2024-02-16.md": "e701902e369ec53098fc2deed4ec14fd", "binary/integer-encoding.md": "7ace6ab6c5a4191ae0abdfe7e5abb6a2", - "combinatorics/index.md": "9a85e8858c50c9797243d6d01e1dcbe7", + "combinatorics/index.md": "200f23380b0817cc13a9acd40996b125", "_journal/2024-02-18.md": "67e36dbbb2cac699d4533b5a2eaeb629", "_journal/2024-02/2024-02-17.md": "7c37cb10515ed3d2f5388eaf02a67048", "combinatorics/multiplicative-principle.md": "f1430302e0a35b863fa965a834c4e40a", diff --git a/notes/combinatorics/images/ordering-n-repetition-n.jpg b/notes/combinatorics/images/ordering-n-repetition-n.jpg new file mode 100644 index 0000000..4955fcc Binary files /dev/null and b/notes/combinatorics/images/ordering-n-repetition-n.jpg differ diff --git a/notes/combinatorics/images/ordering-n-repetition-y.jpg b/notes/combinatorics/images/ordering-n-repetition-y.jpg new file mode 100644 index 0000000..3799a20 Binary files /dev/null and b/notes/combinatorics/images/ordering-n-repetition-y.jpg differ diff --git a/notes/combinatorics/images/ordering-repetition.jpg b/notes/combinatorics/images/ordering-repetition.jpg new file mode 100644 index 0000000..4d38227 Binary files /dev/null and b/notes/combinatorics/images/ordering-repetition.jpg differ diff --git a/notes/combinatorics/images/ordering-y-repetition-n.jpg b/notes/combinatorics/images/ordering-y-repetition-n.jpg new file mode 100644 index 0000000..1dbfaf0 Binary files /dev/null and b/notes/combinatorics/images/ordering-y-repetition-n.jpg differ diff --git a/notes/combinatorics/images/ordering-y-repetition-y.jpg b/notes/combinatorics/images/ordering-y-repetition-y.jpg new file mode 100644 index 0000000..6673988 Binary files /dev/null and b/notes/combinatorics/images/ordering-y-repetition-y.jpg differ diff --git a/notes/combinatorics/index.md b/notes/combinatorics/index.md index de5ec68..c38ea62 100644 --- a/notes/combinatorics/index.md +++ b/notes/combinatorics/index.md @@ -36,34 +36,110 @@ END%% %%ANKI Basic -If order matters and repeats are allowed, the number of selections is usually formatted in what way? +What combinatorial *notation* corresponds to the highlighted square? +![[ordering-y-repetition-y.jpg]] Back: $n^k$ 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). - + END%% %%ANKI Basic -If order matters and repeats are disallowed, the number of selections is usually formatted in what way? -Back: $(n)_k$ (falling factorial) +What combinatorial *concept* corresponds to the highlighted square? +![[ordering-y-repetition-y.jpg]] +Back: The multiplicative principle. 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). - + END%% %%ANKI Basic -If order does not matter and repeats are allowed, the number of selections is usually formatted in what way? -Back: $\binom{n + k}{k}$ (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). - +Which square corresponds to notation $n^k$? +![[ordering-repetition.jpg]] +Back: +![[ordering-y-repetition-y.jpg]] + END%% %%ANKI Basic -If order does not matter and repeats are disallowed, the number of selections is usually formatted in what way? -Back: $\binom{n}{k}$ (combinations) +What combinatorial *notation* corresponds to the highlighted square? +![[ordering-y-repetition-n.jpg]] +Back: $(n)_k$ 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). - + +END%% + +%%ANKI +Basic +What combinatorial *concept* corresponds to the highlighted square? +![[ordering-y-repetition-n.jpg]] +Back: $k$-permutations (falling factorials) +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). + +END%% + +%%ANKI +Basic +Which square corresponds to notation $(n)_k$? +![[ordering-repetition.jpg]] +Back: +![[ordering-y-repetition-n.jpg]] + +END%% + +%%ANKI +Basic +What combinatorial *notation* corresponds to the highlighted square? +![[ordering-n-repetition-y.jpg]] +Back: $\binom{n + k}{k}$ +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). + +END%% + +%%ANKI +Basic +What combinatorial *concept* corresponds to the highlighted square? +![[ordering-n-repetition-y.jpg]] +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). + +END%% + +%%ANKI +Basic +Which square corresponds to notation $\binom{n + k}{k}$? +![[ordering-repetition.jpg]] +Back: +![[ordering-n-repetition-y.jpg]] + +END%% + +%%ANKI +Basic +What combinatorial *notation* corresponds to the highlighted square? +![[ordering-n-repetition-n.jpg]] +Back: $\binom{n}{k}$ +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). + +END%% + +%%ANKI +Basic +What combinatorial *concept* corresponds to the highlighted square? +![[ordering-n-repetition-n.jpg]] +Back: Combinations +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). + +END%% + +%%ANKI +Basic +Which square corresponds to notation $\binom{n}{k}$? +![[ordering-repetition.jpg]] +Back: +![[ordering-n-repetition-n.jpg]] + END%% ## References