User Ira Gessel

65 votes

Accepted

Reason for breakdown of a nice binomial identity

answered Aug 3, 2022 at 16:32

50 votes

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New binomial coefficient identity?

answered Jan 30, 2018 at 14:13

40 votes

The "square root" of a graph?

answered Mar 2, 2021 at 1:28

32 votes

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Integrality of a sequence formed by sums

answered Jul 22, 2021 at 0:18

30 votes

Accepted

The Matrix-Tree Theorem without the matrix

answered Aug 22, 2011 at 18:40

29 votes

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Derivative formula

answered Feb 14, 2017 at 20:23

25 votes

Accepted

Eulerian number identity

answered Apr 20, 2019 at 14:34

25 votes

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Combinatorial meaning of the functional equation for logarithm

answered Nov 16, 2012 at 17:50

25 votes

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Can a Bell number be a power of 2?

answered Aug 16, 2023 at 21:54

24 votes

Number of closed walks on an $n$-cube

answered Aug 1, 2011 at 15:50

24 votes

power series of the reciprocal... does a recursive formula exist for the coefficients

answered Jan 26, 2011 at 21:22

24 votes

Accepted

A special binomial identity in need of a proof

answered Jan 30, 2017 at 4:44

23 votes

Does the formal power series solution to $f(f(x))= \sin( x) $ converge?

answered Nov 11, 2010 at 3:53

22 votes

Extremely messy proofs

answered Jan 14, 2011 at 16:42

22 votes

Fibonacci series captures Euler $e=2.718\dots$

answered Apr 15, 2017 at 14:16

22 votes

Proving an identity about Catalan numbers

answered May 6, 2023 at 22:11

20 votes

Summing infinitely many infinitesimally small variables makes sense in algebra

answered Jun 20, 2020 at 17:10

18 votes

Accepted

Arithmetic problem for bicolored graphs

answered Apr 9, 2017 at 15:47

18 votes

Accepted

A particular combinatorial proof of Wilson's theorem

answered Feb 2, 2011 at 3:48

17 votes

Analogue of Fermat's "little" theorem

answered Jun 14, 2022 at 17:55

16 votes

Accepted

Laurent series in several complex variables

answered Sep 25, 2022 at 12:48

16 votes

Show that this ratio of factorials is always an integer

answered May 12, 2013 at 15:00

16 votes

Combinatorial Morse functions and random permutations

answered Jul 9, 2014 at 16:27

15 votes

Use of everywhere divergent generating functions

answered Nov 13, 2010 at 18:50

14 votes

Number of integer combinations $x_1 < \cdots < x_n$?

answered Jan 18, 2012 at 15:58

14 votes

On the polynomial $\sum_{k=0}^n\binom{n}{k}(-1)^kX^{k(n-k)}$

answered Apr 1, 2018 at 19:50

14 votes

Accepted

Series involving factorials

answered Jan 1, 2018 at 14:42

14 votes

Accepted

Is this formal noncommutative power series identity known?

answered Jun 23, 2020 at 16:59

13 votes

Looking for a combinatorial proof for a Catalan identity

answered Feb 8, 2021 at 0:39

13 votes

Accepted

The combinatorial interpretation of an identity found in "Primes in tuples I"

answered Nov 22, 2013 at 4:49

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191 Answers

Reason for breakdown of a nice binomial identity

New binomial coefficient identity?

The "square root" of a graph?

Integrality of a sequence formed by sums

The Matrix-Tree Theorem without the matrix

Derivative formula

Eulerian number identity

Combinatorial meaning of the functional equation for logarithm

Can a Bell number be a power of 2?

Number of closed walks on an $n$-cube

power series of the reciprocal... does a recursive formula exist for the coefficients

A special binomial identity in need of a proof

Does the formal power series solution to $f(f(x))= \sin( x) $ converge?

Extremely messy proofs

Fibonacci series captures Euler $e=2.718\dots$

Proving an identity about Catalan numbers

Summing infinitely many infinitesimally small variables makes sense in algebra

Arithmetic problem for bicolored graphs

A particular combinatorial proof of Wilson's theorem

Analogue of Fermat's "little" theorem

Laurent series in several complex variables

Show that this ratio of factorials is always an integer

Combinatorial Morse functions and random permutations

Use of everywhere divergent generating functions

Number of integer combinations $x_1 < \cdots < x_n$?

On the polynomial $\sum_{k=0}^n\binom{n}{k}(-1)^kX^{k(n-k)}$

Series involving factorials

Is this formal noncommutative power series identity known?

Looking for a combinatorial proof for a Catalan identity

The combinatorial interpretation of an identity found in "Primes in tuples I"