Question

Show by combinatorial proof that for $n \geq 4$, $3 {n \choose 4} + 3{n\choose 3} = {{n \choose 2} \choose 2}$

score 329 · Answer 1 · 2020-10-21 02:26:02

329

Views

Show by combinatorial proof that for $n \geq 4$, $3 {n \choose 4} + 3{n\choose 3} = {{n \choose 2} \choose 2}$

Published on 21 Oct 2020 - 2:26

score 212 · Answer 2 · 2020-10-21 16:21:00

212

Views

What is a combinatorial proof for the Fibonacci identity $F^2_{n+1} - F^2_{n-1} = F_{2n}$?

Published on 21 Oct 2020 - 16:21

score 139 · Answer 3 · 2026-03-28 23:10:39

139

Views

Closed formula to $N:=\sum_{j=0}^{k/2}\left(\begin{array}{c} n \\ k-j \end{array}\right)\left(\begin{array}{c} k-j \\ j \end{array}\right) $

Published on 28 Mar 2026 - 23:10

score 78 · Answer 4 · 2020-10-22 02:40:09

78

Views

Show that for any $n\geq 0$, the Fibonacci numbers $f_{2n}$ satisfy $f_{2n}=\sum\limits_{k=0}^n\binom{n+k}{2k}$

Published on 22 Oct 2020 - 2:40

score 162 · Answer 5 · 2020-10-22 07:47:00

162

Views

Combinatorial interpretation for $\binom{n}{3}- \lfloor \frac{n}{3} \rfloor$

Published on 22 Oct 2020 - 7:47

score 157 · Answer 6 · 2026-03-27 10:12:55

157

Views

I need a combinatorial proof of $\sum_{n_1+n_2+n_3=n} \binom{n}{n_1, n_2,n_3}(-1)^{n_2} = 1$

Published on 27 Mar 2026 - 10:12

score 96 · Answer 7 · 2020-10-25 12:09:24

96

Views

How do you solve this binomial proof?

Published on 25 Oct 2020 - 12:09

score 128 · Answer 8 · 2026-03-25 23:11:02

128

Views

Checking an "equivalence of products" in the notes on deformation quantization by Allen C. Hirshfeld and Peter Henselder

Published on 25 Mar 2026 - 23:11

score 244 · Answer 9 · 2026-03-28 14:25:42

244

Views

Combinatorial proof for a Fibonacci identity

Published on 28 Mar 2026 - 14:25

score 144 · Answer 10 · 2026-03-29 16:34:42

144

Views

Catalan identity to calculate the determinant of a matrix.

Published on 29 Mar 2026 - 16:34

score 284 · Answer 11 · 2026-03-27 10:44:38

284

Views

How many ways to form a binary sequence with 0 and 1, where no 3 consecutive digits are 1? (without recurrence)

Published on 27 Mar 2026 - 10:44

score 483 · Answer 12 · 2020-10-29 13:20:36

483

Views

compositions of n into even parts

Published on 29 Oct 2020 - 13:20

score 136 · Answer 13 · 2020-10-30 00:10:06

136

Views

if $n>0$ and $r>0$ ($n$ and $r$ and positive integers) and $r$ divides $n$ , then $n/r$ divides $nCr$ . Is this statement true?

Published on 30 Oct 2020 - 0:10

score 27 · Answer 14 · 2020-10-30 17:39:45

27

Views

Showing there always exists a sequence of numbers in an arbitrary list that sums to a certain value

Published on 30 Oct 2020 - 17:39

score 80 · Answer 15 · 2020-11-01 03:37:54

80

Views

Probability of winning half the matchups in a dance competition

Published on 01 Nov 2020 - 3:37

List Question

Show by combinatorial proof that for $n \geq 4$, $3 {n \choose 4} + 3{n\choose 3} = {{n \choose 2} \choose 2}$

What is a combinatorial proof for the Fibonacci identity $F^2_{n+1} - F^2_{n-1} = F_{2n}$?

Closed formula to $N:=\sum_{j=0}^{k/2}\left(\begin{array}{c} n \\ k-j \end{array}\right)\left(\begin{array}{c} k-j \\ j \end{array}\right) $

Show that for any $n\geq 0$, the Fibonacci numbers $f_{2n}$ satisfy $f_{2n}=\sum\limits_{k=0}^n\binom{n+k}{2k}$

Combinatorial interpretation for $\binom{n}{3}- \lfloor \frac{n}{3} \rfloor$

I need a combinatorial proof of $\sum_{n_1+n_2+n_3=n} \binom{n}{n_1, n_2,n_3}(-1)^{n_2} = 1$

How do you solve this binomial proof?

Checking an "equivalence of products" in the notes on deformation quantization by Allen C. Hirshfeld and Peter Henselder

Combinatorial proof for a Fibonacci identity

Catalan identity to calculate the determinant of a matrix.

How many ways to form a binary sequence with 0 and 1, where no 3 consecutive digits are 1? (without recurrence)

compositions of n into even parts

if $n>0$ and $r>0$ ($n$ and $r$ and positive integers) and $r$ divides $n$ , then $n/r$ divides $nCr$ . Is this statement true?

Showing there always exists a sequence of numbers in an arbitrary list that sums to a certain value

Probability of winning half the matchups in a dance competition

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