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

Sela Fried

Research output: Contribution to journalArticlepeer-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 +···+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.

Original languageEnglish
Article number22.4.2
JournalJournal of Integer Sequences
Volume25
Issue number4
StatePublished - 1 Jan 2022

Keywords

  • Catalan number
  • combinatorial optimization problem
  • integer partition
  • multivariate polynomial

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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