Mathematics
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Phicar
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All Questions Answers
Score Newest
answer
10
Give combinatorial a proof that $\binom{n}{2}^2=\binom{n}{2}+6\binom{n}{3}+6\binom{n}{4}$
Jul 28, 2022
question
9
Examples of Manifolds such that $\chi (X)=-3$
Apr 30, 2016
answer
7
Proof of identity relating Prime-counting function and Stirling numbers of the second kind
Jun 30, 2020
answer
7
Prove that $(-1)^n \text{Laguerre}_n(2) \leq 1$.
Nov 3, 2020
answer
7
Help in simplifying combinatorial sum $\frac{n!}{(n-k)!}-{1\over(n-k)!}{\sum _{m=1}^{k-1} (-1)^{m+1} (n-m)! S(k,k-m)}$
Jul 10, 2020
answer
7
Can this be proved using Combinatorics or generating functions?
Nov 24, 2020
answer
7
If a power of 2 divides a number, under what conditions does it divide a binomial coefficient involving the number that it divides?
Nov 11, 2020
answer
6
Combinatorial proof of $\sum_{k=0}^{n} k \binom{n+1}{k+1} n^{n-k} = n^{n+1}$
Apr 11, 2022
answer
6
Is there an expression for the coefficients of the falling factorial $x^{\underline n} \equiv x (x-1) \dots (x-n+1)$?
Apr 17, 2020
answer
6
Proving identity through combinatorial model
Nov 23, 2020

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