Question

Bijection between powerset and increasing-ordered tuples

score 45 · Answer 1 · 2021-09-20 08:54:14

45

Views

Bijection between powerset and increasing-ordered tuples

Published on 20 Sep 2021 - 8:54

score 59 · Answer 2 · 2021-09-20 13:49:42

59

Views

How to proof this polynomial sum formula?

Published on 20 Sep 2021 - 13:49

score 300 · Answer 3 · 2021-09-20 22:46:12

300

Views

If $H$ is a connected subgraph of $G$ show that $T(H)\le T(G)$.

Published on 20 Sep 2021 - 22:46

score 158 · Answer 4 · 2021-09-21 13:21:07

158

Views

Proving an identity relating to binomial coefficients

Published on 21 Sep 2021 - 13:21

score 97 · Answer 5 · 2021-09-21 18:46:13

97

Views

Combinatorial proof for $n\ge1$ of $3^n = \sum_{k=0}^n \binom{n}{k}(2^{n-k})$

Published on 21 Sep 2021 - 18:46

score 101 · Answer 6 · 2021-09-21 19:59:06

101

Views

Combinatorially counting the Riemann tensor's degrees of freedom

Published on 21 Sep 2021 - 19:59

score 107 · Answer 7 · 2021-09-27 04:49:08

107

Views

Give a combinatorial proof for the expression $\sum_{k=0}^{n-1} 2^k = 2^n - 1$

Published on 27 Sep 2021 - 4:49

score 360 · Answer 8 · 2021-10-03 07:27:38

360

Views

A combinatorial question about odd and even numbers

Published on 03 Oct 2021 - 7:27

score 128 · Answer 9 · 2021-10-04 19:39:53

128

Views

Let g_n equal the number of lists of any length taken from {1,3,4} having elements that sum to n.

Published on 04 Oct 2021 - 19:39

score 26 · Answer 10 · 2026-03-30 00:20:00

26

Views

Counting integer vectors of given length inside particular area/ special number compositions

Published on 30 Mar 2026 - 0:20

score 154 · Answer 11 · 2021-10-09 18:38:04

154

Views

Combinatorial proofs that $\binom{2^n}{k}$ is even for every $n\geq 1$ and $1\leq k \leq 2^n-1$.

Published on 09 Oct 2021 - 18:38

score 122 · Answer 12 · 2021-10-10 21:53:32

122

Views

For n $\geq$ k, what is $\sum_{i=1}^n (-1)^i {n \choose i} i^k$?

Published on 10 Oct 2021 - 21:53

score 64 · Answer 13 · 2021-10-11 19:54:21

64

Views

What is $\sum_{k=0}^{n} {n \choose k}^3$

Published on 11 Oct 2021 - 19:54

score 40 · Answer 14 · 2021-10-13 23:29:55

40

Views

Prove for x real and p integer that $\begin{pmatrix}x\\ p\end{pmatrix}=\left(-1\right)^p\:\cdot \begin{pmatrix}p-x-1\\ \:p\end{pmatrix}$

Published on 13 Oct 2021 - 23:29

score 69 · Answer 15 · 2021-10-14 07:23:19

69

Views

Chebyshev polynomials and ballot number

Published on 14 Oct 2021 - 7:23

List Question

Bijection between powerset and increasing-ordered tuples

How to proof this polynomial sum formula?

If $H$ is a connected subgraph of $G$ show that $T(H)\le T(G)$.

Proving an identity relating to binomial coefficients

Combinatorial proof for $n\ge1$ of $3^n = \sum_{k=0}^n \binom{n}{k}(2^{n-k})$

Combinatorially counting the Riemann tensor's degrees of freedom

Give a combinatorial proof for the expression $\sum_{k=0}^{n-1} 2^k = 2^n - 1$

A combinatorial question about odd and even numbers

Let g_n equal the number of lists of any length taken from {1,3,4} having elements that sum to n.

Counting integer vectors of given length inside particular area/ special number compositions

Combinatorial proofs that $\binom{2^n}{k}$ is even for every $n\geq 1$ and $1\leq k \leq 2^n-1$.

For n $\geq$ k, what is $\sum_{i=1}^n (-1)^i {n \choose i} i^k$?

What is $\sum_{k=0}^{n} {n \choose k}^3$

Prove for x real and p integer that $\begin{pmatrix}x\\ p\end{pmatrix}=\left(-1\right)^p\:\cdot \begin{pmatrix}p-x-1\\ \:p\end{pmatrix}$

Chebyshev polynomials and ballot number

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