Question

Combinatorial approach to prove divisibility results with the sequence $u_{n+p+1} = u_{n+p} + u_{n}$ in $\mathbb{F}_p$

score 87 · Answer 1 · 2020-01-01 23:37:30

87

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Combinatorial approach to prove divisibility results with the sequence $u_{n+p+1} = u_{n+p} + u_{n}$ in $\mathbb{F}_p$

Published on 01 Jan 2020 - 23:37

score 258 · Answer 2 · 2020-01-05 04:45:34

258

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Prove that $\sum_{k=0}^{\lfloor (n-1)/2 \rfloor} (-1)^k {n+1 \choose k} {2n-2k-1 \choose n} =\frac{ n(n+1)}2 $

Published on 05 Jan 2020 - 4:45

score 634 · Answer 3 · 2026-03-25 19:04:28

634

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Number of matchings in a cycle graph

Published on 25 Mar 2026 - 19:04

score 1.1k · Answer 4 · 2020-01-12 01:00:14

Combinatorics: Bijective proof for ${n + t - 1 \choose t - 1} = \sum_{k=0}^n{n-k+t-2 \choose t-2}$ for integers ${n\ge 1}$, ${t\ge 2}$

score 207 · Answer 5 · 2020-01-12 15:43:23

207

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How should I solve combination addition like this?

Published on 12 Jan 2020 - 15:43

score 205 · Answer 6 · 2020-01-14 02:59:35

205

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Proof for $\sum_{k=1}^n k2^k \binom{2n-k-1}{n-1} = n\binom{2n}{n}$?

Published on 14 Jan 2020 - 2:59

score 106 · Answer 7 · 2026-03-25 10:59:48

106

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Combinatorial bijection of primitive factorization

Published on 25 Mar 2026 - 10:59

score 109 · Answer 8 · 2020-01-17 10:09:44

109

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Calculate $\sum_1^{30}r^3 {30 \choose r}$

Published on 17 Jan 2020 - 10:09

score 110 · Answer 9 · 2020-01-18 00:01:42

110

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Cardinality of ordered pairs of subsets of {1, ..., n} computed in 2 different ways

Published on 18 Jan 2020 - 0:01

score 43 · Answer 10 · 2020-01-18 21:35:03

43

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Exponential family hypercube summation identity

Published on 18 Jan 2020 - 21:35

score 68 · Answer 11 · 2020-01-19 19:42:38

68

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What does the equation imply combinatorially $\frac{1}{(1 - x)^t} = \frac{(1 - x)^c}{(1 - x)^{t + c}}$

Published on 19 Jan 2020 - 19:42

score 126 · Answer 12 · 2020-01-20 21:38:48

126

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Combinatorial Proof ${n \choose k}\cdot (n-k)\cdot 2^{k} = \sum_{i=1}^{k+1} {n\choose i}\cdot{n-i\choose k-i+1}\cdot i $

Published on 20 Jan 2020 - 21:38

score 304 · Answer 13 · 2020-01-21 14:37:13

304

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A second formula for the dimension of the symmetric tensor product? ... (No)

Published on 21 Jan 2020 - 14:37

score 166 · Answer 14 · 2020-01-25 02:52:50

166

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Series prove using combinational argument

Published on 25 Jan 2020 - 2:52

score 61 · Answer 15 · 2020-01-25 05:05:54

61

Views

Win Conditions for Single Pile NIM (players can only take a or b stones from the pile on each turn)

Published on 25 Jan 2020 - 5:05

List Question

Combinatorial approach to prove divisibility results with the sequence $u_{n+p+1} = u_{n+p} + u_{n}$ in $\mathbb{F}_p$

Prove that $\sum_{k=0}^{\lfloor (n-1)/2 \rfloor} (-1)^k {n+1 \choose k} {2n-2k-1 \choose n} =\frac{ n(n+1)}2 $

Number of matchings in a cycle graph

Combinatorics: Bijective proof for ${n + t - 1 \choose t - 1} = \sum_{k=0}^n{n-k+t-2 \choose t-2}$ for integers ${n\ge 1}$, ${t\ge 2}$

How should I solve combination addition like this?

Proof for $\sum_{k=1}^n k2^k \binom{2n-k-1}{n-1} = n\binom{2n}{n}$?

Combinatorial bijection of primitive factorization

Calculate $\sum_1^{30}r^3 {30 \choose r}$

Cardinality of ordered pairs of subsets of {1, ..., n} computed in 2 different ways

Exponential family hypercube summation identity

What does the equation imply combinatorially $\frac{1}{(1 - x)^t} = \frac{(1 - x)^c}{(1 - x)^{t + c}}$

Combinatorial Proof ${n \choose k}\cdot (n-k)\cdot 2^{k} = \sum_{i=1}^{k+1} {n\choose i}\cdot{n-i\choose k-i+1}\cdot i $

A second formula for the dimension of the symmetric tensor product? ... (No)

Series prove using combinational argument

Win Conditions for Single Pile NIM (players can only take a or b stones from the pile on each turn)

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