Question

Prove that the probabilities that the sum of the elements of the chosen subset is congruent to 0,1,2 mod 3 are equal iff $k\equiv 1,2\mod 3$

score 93 · Answer 1 · 2023-10-20 18:19:07

93

Views

Prove that the probabilities that the sum of the elements of the chosen subset is congruent to 0,1,2 mod 3 are equal iff $k\equiv 1,2\mod 3$

Published on 20 Oct 2023 - 18:19

score 95 · Answer 2 · 2023-10-20 23:07:26

95

Views

From a Sequence to Taylor Series

Published on 20 Oct 2023 - 23:07

score 103 · Answer 3 · 2026-03-28 14:55:10

103

Views

Finding the number of integer composition using only a specific pair of numbers

Published on 28 Mar 2026 - 14:55

score 96 · Answer 4 · 2023-10-21 14:39:48

96

Views

How do we use generating functions to find letter permutations?

Published on 21 Oct 2023 - 14:39

score 160 · Answer 5 · 2023-10-21 16:50:05

160

Views

Selecting $k$ elements from the set $[n]$ such that the numbers selected differ by at least three

Published on 21 Oct 2023 - 16:50

score 53 · Answer 6 · 2026-03-28 10:03:53

53

Views

Prove that $a_n=a_{n-1}$

Published on 28 Mar 2026 - 10:03

score 74 · Answer 7 · 2026-03-26 10:59:45

74

Views

What is the combinatorics meaning of the generating function for Legendre polynomials?

Published on 26 Mar 2026 - 10:59

score 48 · Answer 8 · 2023-10-22 13:48:52

48

Views

Prove that $g(x)_n = f(x)_{n+1}$

Published on 22 Oct 2023 - 13:48

score 158 · Answer 9 · 2023-10-22 20:27:30

158

Views

$A'(x) = 2xA(x)$. Find a closed formula for $A(x)$.

Published on 22 Oct 2023 - 20:27

score 23 · Answer 10 · 2023-10-23 17:38:53

23

Views

Stirling number of first kind identity

Published on 23 Oct 2023 - 17:38

score 44 · Answer 11 · 2023-10-24 11:13:07

44

Views

Find the ordinary generating function of given sequence

Published on 24 Oct 2023 - 11:13

score 81 · Answer 12 · 2023-10-25 16:57:25

81

Views

What is wrong with my solution? Splitting the set [n] into non-empty intervals and choosing a non-empty subset from these intervals

Published on 25 Oct 2023 - 16:57

score 46 · Answer 13 · 2023-10-26 22:33:06

Number of ways for splitting elements into non-empty subsets, forming a line within eachnsubset, then arranging the subsets in a line

score 81 · Answer 14 · 2023-10-28 12:13:57

81

Views

Find the generator function

Published on 28 Oct 2023 - 12:13

score 118 · Answer 15 · 2023-10-29 16:16:11

118

Views

Solve generating function in recurring form

Published on 29 Oct 2023 - 16:16

List Question

Prove that the probabilities that the sum of the elements of the chosen subset is congruent to 0,1,2 mod 3 are equal iff $k\equiv 1,2\mod 3$

From a Sequence to Taylor Series

Finding the number of integer composition using only a specific pair of numbers

How do we use generating functions to find letter permutations?

Selecting $k$ elements from the set $[n]$ such that the numbers selected differ by at least three

Prove that $a_n=a_{n-1}$

What is the combinatorics meaning of the generating function for Legendre polynomials?

Prove that $g(x)_n = f(x)_{n+1}$

$A'(x) = 2xA(x)$. Find a closed formula for $A(x)$.

Stirling number of first kind identity

Find the ordinary generating function of given sequence

What is wrong with my solution? Splitting the set [n] into non-empty intervals and choosing a non-empty subset from these intervals

Number of ways for splitting elements into non-empty subsets, forming a line within eachnsubset, then arranging the subsets in a line

Find the generator function

Solve generating function in recurring form

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