On the Coefficients of the Distinct Monomials in the Expansion of x1(x1 +x2)···(x1 +x2 +···+xn)

Sela Fried

On the Coefficients of the Distinct Monomials in the Expansion of x₁(x₁ +x₂)···(x₁ +x₂ +···+x_n)

Sela Fried

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

We initiate the study of the coefficients of the distinct monomials in the expansion of the multivariate polynomials x₁(x₁ +x₂)···(x₁ +x₂ +···+x_n),n ∈ ℕ, the number of which was shown by Shallit to be counted by the Catalan numbers C_n,n ∈ ℕ. In particular, we obtain an exact formula for the coefficients and reduce the complexity of the search for their maximum from the order of C_n to the order of the number of partitions of n with distinct parts.

Original language	English
Article number	22.4.2
Journal	Journal of Integer Sequences
Volume	25
Issue number	4
State	Published - 1 Jan 2022

Keywords

Catalan number
combinatorial optimization problem
integer partition
multivariate polynomial

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

Cite this

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AB - We initiate the study of the coefficients of the distinct monomials in the expansion of the multivariate polynomials x1(x1 +x2)···(x1 +x2 +···+xn),n ∈ ℕ, the number of which was shown by Shallit to be counted by the Catalan numbers Cn,n ∈ ℕ. In particular, we obtain an exact formula for the coefficients and reduce the complexity of the search for their maximum from the order of Cn to the order of the number of partitions of n with distinct parts.

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KW - combinatorial optimization problem

KW - integer partition

KW - multivariate polynomial

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ER -

On the Coefficients of the Distinct Monomials in the Expansion of x₁(x₁ +x₂)···(x₁ +x₂ +···+x_n)

Abstract

Keywords

ASJC Scopus subject areas

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