Question

Number of compositions of $n$ where each part is at least $m$

score 89 · Answer 1 · 2024-03-04 16:53:14

89

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Number of compositions of $n$ where each part is at least $m$

Published on 04 Mar 2024 - 16:53

score 44 · Answer 2 · 2026-02-23 16:53:29

44

Views

generating function, compositions odd, congruence modulo

Published on 23 Feb 2026 - 16:53

score 16 · Answer 3 · 2024-03-05 18:29:39

16

Views

compositions of $n$ each part at least $c$

Published on 05 Mar 2024 - 18:29

score 39 · Answer 4 · 2026-03-19 14:39:24

39

Views

Probability Theory: Generating Functions of Random Variables

Published on 19 Mar 2026 - 14:39

score 30 · Answer 5 · 2024-03-08 12:14:24

30

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Derivative of the generating function

Published on 08 Mar 2024 - 12:14

score 90 · Answer 6 · 2024-03-08 20:35:14

90

Views

Find the generating function for $a_n=\sum_{k=0}^{n} 3^{k}(n-k), n\geq0$.

Published on 08 Mar 2024 - 20:35

score 129 · Answer 7 · 2024-03-11 10:55:01

129

Views

Find the coefficient of $x^{30}$ in the following polynomial $(1+x+x^2+x^3+x^4+x^6)^6$

Published on 11 Mar 2024 - 10:55

score 60 · Answer 8 · 2024-03-12 12:40:52

60

Views

How many ways are there to distribute $19$ distinct objects into $3$ distinct boxes such that no two boxes contain same number of element

Published on 12 Mar 2024 - 12:40

score 96 · Answer 9 · 2026-03-28 13:32:17

96

Views

Generating Functions for Recursive String Compositions with Parenthetical Constraints

Published on 28 Mar 2026 - 13:32

score 151 · Answer 10 · 2026-02-23 13:45:55

151

Views

Prove that $b_n = [x^n]\frac{1-x^2+x^3}{1-2x+x^2-x^3}$

Published on 23 Feb 2026 - 13:45

score 118 · Answer 11 · 2026-03-26 17:27:44

118

Views

Generating function for binary strings not containing $0110$ or $11010$ as a substring

Published on 26 Mar 2026 - 17:27

score 415 · Answer 12 · 2024-03-17 06:43:53

415

Views

Number of elements in set $S = \{(x,y,z): x,y,z \in \mathbb{Z}, x+2y+3z=42, x,y,z \ge 0\}$ is?

Published on 17 Mar 2024 - 6:43

score 55 · Answer 13 · 2024-03-17 13:46:48

55

Views

Find generating function of $\frac{5-3x}{2-3x+x^2}$.

Published on 17 Mar 2024 - 13:46

score 31 · Answer 14 · 2024-03-18 19:14:02

31

Views

Ordinary generating functions and Stieltjes-Perron Inversion Theorem

Published on 18 Mar 2024 - 19:14

score 69 · Answer 15 · 2026-03-28 13:59:37

69

Views

How to show that two generating functions share congruent coefficients

Published on 28 Mar 2026 - 13:59

List Question

Number of compositions of $n$ where each part is at least $m$

generating function, compositions odd, congruence modulo

compositions of $n$ each part at least $c$

Probability Theory: Generating Functions of Random Variables

Derivative of the generating function

Find the generating function for $a_n=\sum_{k=0}^{n} 3^{k}(n-k), n\geq0$.

Find the coefficient of $x^{30}$ in the following polynomial $(1+x+x^2+x^3+x^4+x^6)^6$

How many ways are there to distribute $19$ distinct objects into $3$ distinct boxes such that no two boxes contain same number of element

Generating Functions for Recursive String Compositions with Parenthetical Constraints

Prove that $b_n = [x^n]\frac{1-x^2+x^3}{1-2x+x^2-x^3}$

Generating function for binary strings not containing $0110$ or $11010$ as a substring

Number of elements in set $S = \{(x,y,z): x,y,z \in \mathbb{Z}, x+2y+3z=42, x,y,z \ge 0\}$ is?

Find generating function of $\frac{5-3x}{2-3x+x^2}$.

Ordinary generating functions and Stieltjes-Perron Inversion Theorem

How to show that two generating functions share congruent coefficients

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