List questions from combinatorics

Published on 12 Apr 2026 - 5:14

274

Views

To prove: $n!=\sum\limits_{r=0}^n (-1)^r \binom{n}{r} (n-r)^n$

Published on 15 Apr 2026 - 20:22

226

Views

Interlacing two ordered sequences with constraints

Published on 11 Apr 2026 - 18:56

263

Views

Betting on intervals

Published on 05 Apr 2026 - 10:45

5k

Views

5 persons and 5 chairs

Published on 15 Apr 2026 - 21:53

1.4k

Views

Bijection $f\colon\mathbb{N}\to\mathbb{N}$ with $f(0)=0$ and $|f(n)-f(n-1)|=n$

Published on 17 Apr 2026 - 15:50

160

Views

Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$

Published on 26 Mar 2026 - 17:53

131

Views

Formal power series: $F_i(x)$ converges if and only if $\lim_{i\to\infty}deg(F_{i+1}(x)- F_i(x))=\infty.$

Published on 17 Apr 2026 - 11:11

450

Views

Recurrence for Number of Words of Length $r$ over $[n]$ with no three consecutive letters the same

Published on 15 Apr 2026 - 13:07

138

Views

Why does the Fibonacci sequence seem to have such a rich theory?

Published on 14 Apr 2026 - 11:26

29

Views

$\mathbb{E}[X_1|X_2]$ of permutation on $9$ elements

Published on 16 Apr 2026 - 9:03

108

Views

An urn with three kinds of balls... and a weird constraint!

Published on 14 Apr 2026 - 5:15

76

Views

Prove: the number of simple undirected graphs with n different nodes, s.t every node has even degree is $2^\binom{n-1}{2}$

Published on 16 Apr 2026 - 11:08

47

Views

How many ways can we distribute 10 toys, 5 balls and 7 rings to 3 children?

Published on 15 Apr 2026 - 0:13

48

Views

Asymptotic basis of order 3

Published on 15 Apr 2026 - 11:14

List Question

Probability of a structure of consecutive head tosses

To prove: $n!=\sum\limits_{r=0}^n (-1)^r \binom{n}{r} (n-r)^n$

Interlacing two ordered sequences with constraints

Betting on intervals

5 persons and 5 chairs

Bijection $f\colon\mathbb{N}\to\mathbb{N}$ with $f(0)=0$ and $|f(n)-f(n-1)|=n$

Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$

Formal power series: $F_i(x)$ converges if and only if $\lim_{i\to\infty}deg(F_{i+1}(x)- F_i(x))=\infty.$

Recurrence for Number of Words of Length $r$ over $[n]$ with no three consecutive letters the same

Why does the Fibonacci sequence seem to have such a rich theory?

$\mathbb{E}[X_1|X_2]$ of permutation on $9$ elements

An urn with three kinds of balls... and a weird constraint!

Prove: the number of simple undirected graphs with n different nodes, s.t every node has even degree is $2^\binom{n-1}{2}$

How many ways can we distribute 10 toys, 5 balls and 7 rings to 3 children?

Asymptotic basis of order 3

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