Question

Prove by double-counting: $\sum_{k=d} ^n {n \choose k} {k \choose d} = 2^ {(n-d)} {n \choose d} $?

score 166 · Answer 1 · 2026-03-31 14:32:47

166

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Prove by double-counting: $\sum_{k=d} ^n {n \choose k} {k \choose d} = 2^ {(n-d)} {n \choose d} $?

Published on 31 Mar 2026 - 14:32

score 111 · Answer 2 · 2026-03-31 14:30:45

111

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A form has 7 questions, each with 3 possible answers: A , B , or C. How many ways that the answer sheet has the same number of A and B

Published on 31 Mar 2026 - 14:30

score 337 · Answer 3 · 2026-03-31 14:27:09

337

Views

Prove $\sum_ {k=0} ^n {n \choose k}^2 = {2n \choose n} $?

Published on 31 Mar 2026 - 14:27

score 153 · Answer 4 · 2026-03-25 17:45:40

153

Views

Invariants restricting possible similarity matrices to only permutations for graph isomorphism problem?

Published on 25 Mar 2026 - 17:45

score 145 · Answer 5 · 2026-03-25 12:47:03

145

Views

Composition of permutations in factoradic notation

Published on 25 Mar 2026 - 12:47

score 965 · Answer 6 · 2026-03-30 05:13:44

965

Views

Number of six digit numbers divisible by $3$ but none of the digits is $3$

Published on 30 Mar 2026 - 5:13

score 416 · Answer 7 · 2019-05-07 18:54:00

416

Views

Simplifying permutations written in cycle notation

Published on 07 May 2019 - 18:54

score 41 · Answer 8 · 2019-05-08 07:58:40

41

Views

Mathematical expressions for selections

Published on 08 May 2019 - 7:58

score 157 · Answer 9 · 2019-05-08 13:39:19

157

Views

Question on proof: cosets of the alternating group $A_n$

Published on 08 May 2019 - 13:39

score 74 · Answer 10 · 2026-04-02 05:06:52

74

Views

Cycle types of elements of normalizers of point stabilizers of transitive permutation groups

Published on 02 Apr 2026 - 5:06

score 44 · Answer 11 · 2026-04-02 05:01:55

44

Views

Number of permutations $\sigma\in S_n$ with $\sigma(k)\neq k$ for all $k=1,\ldots,n$

Published on 02 Apr 2026 - 5:01

score 105 · Answer 12 · 2026-03-28 00:49:03

105

Views

Decomposition of Cycles (Group Theory Mapping)

Published on 28 Mar 2026 - 0:49

score 94 · Answer 13 · 2026-04-02 05:05:44

94

Views

Cycle types of elements of centralizers of transitive permutation groups

Published on 02 Apr 2026 - 5:05

score 257 · Answer 14 · 2026-03-25 12:46:22

257

Views

How to enumerate Von Dyck groups?

Published on 25 Mar 2026 - 12:46

score 2k · Answer 15 · 2026-03-25 14:07:00

2k

Views

Count the number of permutations of certain cycles type

Published on 25 Mar 2026 - 14:07

List Question

Prove by double-counting: $\sum_{k=d} ^n {n \choose k} {k \choose d} = 2^ {(n-d)} {n \choose d} $?

A form has 7 questions, each with 3 possible answers: A , B , or C. How many ways that the answer sheet has the same number of A and B

Prove $\sum_ {k=0} ^n {n \choose k}^2 = {2n \choose n} $?

Invariants restricting possible similarity matrices to only permutations for graph isomorphism problem?

Composition of permutations in factoradic notation

Number of six digit numbers divisible by $3$ but none of the digits is $3$

Simplifying permutations written in cycle notation

Mathematical expressions for selections

Question on proof: cosets of the alternating group $A_n$

Cycle types of elements of normalizers of point stabilizers of transitive permutation groups

Number of permutations $\sigma\in S_n$ with $\sigma(k)\neq k$ for all $k=1,\ldots,n$

Decomposition of Cycles (Group Theory Mapping)

Cycle types of elements of centralizers of transitive permutation groups

How to enumerate Von Dyck groups?

Count the number of permutations of certain cycles type

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