Question

Combinatorial proof involving partitions and generating functions

score 1k · Answer 1 · 2013-03-18 21:56:13

1k

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Combinatorial proof involving partitions and generating functions

Published on 18 Mar 2013 - 21:56

score 564 · Answer 2 · 2013-03-18 22:26:25

564

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Generating function: number of partitions that add up to at most $n$

Published on 18 Mar 2013 - 22:26

score 210 · Answer 3 · 2013-03-19 08:34:34

210

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Dilworth's Lemma

Published on 19 Mar 2013 - 8:34

score 296 · Answer 4 · 2026-03-29 15:23:13

296

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Determining Stirling number

Published on 29 Mar 2026 - 15:23

score 408 · Answer 5 · 2013-03-21 10:33:15

408

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Balls, Bags, Partitions, and Permutations

Published on 21 Mar 2013 - 10:33

score 743 · Answer 6 · 2013-03-23 22:21:00

743

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Maximal Zero Sums Partition

Published on 23 Mar 2013 - 22:21

score 686 · Answer 7 · 2026-03-25 19:05:03

686

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How to prove it? (one of the Rogers-Ramanujan identities)

Published on 25 Mar 2026 - 19:05

score 716 · Answer 8 · 2013-03-29 08:56:36

716

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bijection between number of partitions of 2n satisfying certain conditions with number of partitions of n

Published on 29 Mar 2013 - 8:56

score 233 · Answer 9 · 2026-03-25 22:10:57

233

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Number of unordered factorizations of a non-square-free positive integer

Published on 25 Mar 2026 - 22:10

score 47 · Answer 10 · 2026-03-31 17:51:37

47

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Calculating the number of ways a set of $n$ numbers with $k$ different possible values can yield a specific average of $m$.

Published on 31 Mar 2026 - 17:51

score 2.3k · Answer 11 · 2020-08-09 00:02:26

2.3k

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How many ordered quadruples $(a,b,c,d)$ satisfy $a+b+c+d=18$ under various conditions?

Published on 09 Aug 2020 - 0:02

score 100 · Answer 12 · 2020-08-09 08:49:12

100

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How many ways are there to add up integers to $n$ such that atleast one of them equals to 1?

Published on 09 Aug 2020 - 8:49

score 79 · Answer 13 · 2020-08-09 17:44:50

79

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On the nonnegative integer solutions that satisfy $\sum x_i \leq n$

Published on 09 Aug 2020 - 17:44

score 234 · Answer 14 · 2020-08-10 03:13:50

234

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$p\equiv 1\pmod 4\Rightarrow p=a^2+b^2$ and $p\equiv 1\pmod 8\Rightarrow p=a^2+2b^2$, what about for $p\equiv 1\pmod {2^n}$ in general

Published on 10 Aug 2020 - 3:13

score 84 · Answer 15 · 2026-03-29 22:27:54

84

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Generating Functions Combinatorial argument

Published on 29 Mar 2026 - 22:27

List Question

Combinatorial proof involving partitions and generating functions

Generating function: number of partitions that add up to at most $n$

Dilworth's Lemma

Determining Stirling number

Balls, Bags, Partitions, and Permutations

Maximal Zero Sums Partition

How to prove it? (one of the Rogers-Ramanujan identities)

bijection between number of partitions of 2n satisfying certain conditions with number of partitions of n

Number of unordered factorizations of a non-square-free positive integer

Calculating the number of ways a set of $n$ numbers with $k$ different possible values can yield a specific average of $m$.

How many ordered quadruples $(a,b,c,d)$ satisfy $a+b+c+d=18$ under various conditions?

How many ways are there to add up integers to $n$ such that atleast one of them equals to 1?

On the nonnegative integer solutions that satisfy $\sum x_i \leq n$

$p\equiv 1\pmod 4\Rightarrow p=a^2+b^2$ and $p\equiv 1\pmod 8\Rightarrow p=a^2+2b^2$, what about for $p\equiv 1\pmod {2^n}$ in general

Generating Functions Combinatorial argument

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