Question

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

score 64 · Answer 1 · 2018-10-05 13:42:57

64

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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 05 Oct 2018 - 13:42

score 791 · Answer 2 · 2018-10-06 12:19:03

791

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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 06 Oct 2018 - 12:19

score 116 · Answer 3 · 2018-10-06 15:13:41

116

Views

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

Published on 06 Oct 2018 - 15:13

score 236 · Answer 4 · 2018-10-09 17:49:48

236

Views

Combinatorial interpretation of alternating sum involving binomial coefficients

Published on 09 Oct 2018 - 17:49

score 223 · Answer 5 · 2018-10-11 18:41:17

223

Views

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

Published on 11 Oct 2018 - 18:41

score 107 · Answer 6 · 2018-10-18 02:43:52

107

Views

Using the Langrange Inversion Formula

Published on 18 Oct 2018 - 2:43

score 157 · Answer 7 · 2026-03-25 04:35:13

157

Views

On the Catalan Numbers

Published on 25 Mar 2026 - 4:35

score 465 · Answer 8 · 2018-10-22 14:00:06

465

Views

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

Published on 22 Oct 2018 - 14:00

score 872 · Answer 9 · 2026-03-25 06:12:05

872

Views

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

Published on 25 Mar 2026 - 6:12

score 104 · Answer 10 · 2018-11-01 07:48:27

104

Views

Combinatorial proofs of several binomial sums

Published on 01 Nov 2018 - 7:48

score 459 · Answer 11 · 2026-03-25 10:52:23

459

Views

Sum of multinomial coefficients

Published on 25 Mar 2026 - 10:52

score 529 · Answer 12 · 2018-11-05 18:28:10

529

Views

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

Published on 05 Nov 2018 - 18:28

score 493 · Answer 13 · 2018-11-06 04:56:09

493

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 06 Nov 2018 - 4:56

score 62 · Answer 14 · 2018-11-10 18:02:25

62

Views

Proving that these two finite alternating series are equal.

Published on 10 Nov 2018 - 18:02

score 276 · Answer 15 · 2026-03-25 06:05:34

276

Views

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

Published on 25 Mar 2026 - 6:05

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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