Question

How to seat guests in circles of chairs if each one wants to have free seats to his left and right?

score 67 · Answer 1 · 2026-04-16 07:17:22

67

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How to seat guests in circles of chairs if each one wants to have free seats to his left and right?

Published on 16 Apr 2026 - 7:17

score 794 · Answer 2 · 2026-04-16 20:42:29

794

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Combinatorics meaning of $L_m=\sum_{j=m}^{n}(-1)^{j-m}\binom{j-1}{m-1}S_j$

Published on 16 Apr 2026 - 20:42

score 119 · Answer 3 · 2026-04-17 03:28:26

119

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A combinatorial inequality $\binom {2n}{k} + \binom {2n}{n-k} \ < \ \binom{2n}{n} + \binom{2n}{0} \ \ \text{for} \ \ k<n \ \ $

Published on 17 Apr 2026 - 3:28

score 239 · Answer 4 · 2026-04-10 11:18:22

239

Views

Combinatorial interpretation of alternating sum involving binomial coefficients

Published on 10 Apr 2026 - 11:18

score 225 · Answer 5 · 2026-04-14 18:21:32

225

Views

Proving If $k \le \left\lfloor \frac{n}{2} \right\rfloor$ then $\binom{n}{k-1} < \binom{n}{k}$

Published on 14 Apr 2026 - 18:21

score 110 · Answer 6 · 2026-04-09 22:14:21

110

Views

Using the Langrange Inversion Formula

Published on 09 Apr 2026 - 22:14

score 161 · Answer 7 · 2026-04-29 12:51:05

161

Views

On the Catalan Numbers

Published on 29 Apr 2026 - 12:51

score 468 · Answer 8 · 2026-04-14 11:43:55

468

Views

A combinatorial proof of determinant as the hyper-volume bounded by vectors?

Published on 14 Apr 2026 - 11:43

score 875 · Answer 9 · 2026-05-10 15:55:06

875

Views

Lower Bound on God's Number in the Rubik's Cube

Published on 10 May 2026 - 15:55

score 107 · Answer 10 · 2026-04-15 10:11:41

107

Views

Combinatorial proofs of several binomial sums

Published on 15 Apr 2026 - 10:11

score 461 · Answer 11 · 2026-05-10 15:44:32

461

Views

Sum of multinomial coefficients

Published on 10 May 2026 - 15:44

score 532 · Answer 12 · 2026-04-12 15:13:11

532

Views

Is there a combinatorial proof that $e$ is finite?

Published on 12 Apr 2026 - 15:13

score 496 · Answer 13 · 2026-04-16 22:13:05

496

Views

How many ways 3 persons A, B , C can be put in a row of six empty chair such that A nd B don't sit together

Published on 16 Apr 2026 - 22:13

score 65 · Answer 14 · 2026-04-15 05:41:42

65

Views

Proving that these two finite alternating series are equal.

Published on 15 Apr 2026 - 5:41

score 280 · Answer 15 · 2026-05-10 15:01:48

280

Views

Show that $1= \sum_{k=0}^{m} (-1)^k {m \choose k}2^{m-k}$ using sign reversing involution

Published on 10 May 2026 - 15:01

List Question

How to seat guests in circles of chairs if each one wants to have free seats to his left and right?

Combinatorics meaning of $L_m=\sum_{j=m}^{n}(-1)^{j-m}\binom{j-1}{m-1}S_j$

A combinatorial inequality $\binom {2n}{k} + \binom {2n}{n-k} \ < \ \binom{2n}{n} + \binom{2n}{0} \ \ \text{for} \ \ k<n \ \ $

Combinatorial interpretation of alternating sum involving binomial coefficients

Proving If $k \le \left\lfloor \frac{n}{2} \right\rfloor$ then $\binom{n}{k-1} < \binom{n}{k}$

Using the Langrange Inversion Formula

On the Catalan Numbers

A combinatorial proof of determinant as the hyper-volume bounded by vectors?

Lower Bound on God's Number in the Rubik's Cube

Combinatorial proofs of several binomial sums

Sum of multinomial coefficients

Is there a combinatorial proof that $e$ is finite?

How many ways 3 persons A, B , C can be put in a row of six empty chair such that A nd B don't sit together

Proving that these two finite alternating series are equal.

Show that $1= \sum_{k=0}^{m} (-1)^k {m \choose k}2^{m-k}$ using sign reversing involution

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