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 language | English |
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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