On the Unimodality of some Partition Polynomials

A. M. Odlyzko, L. B. Richmond

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

It is shown that for a wide class of sequences {ai} of positive integers, the polynomials Π i=1n(1+x ai)=∑ k=0N bkxk,N=∑ i=1n ai are almost unimodal; i.e. there is a constant A, independent of n, such that bA⩽bA+1⩽⋯⩽bK and bK⩾bK+1⩾⋯⩾bN-A, where K=N/2 or (N+1)/2. Among the sequences {ai} to which this result applies are the sequences given by ak=f(k), where f(x) is a polynomial with integer coefficients such that for every prime p there is an integer k with p∤f(k).

Original languageEnglish (US)
Pages (from-to)69-84
Number of pages16
JournalEuropean Journal of Combinatorics
Volume3
Issue number1
DOIs
StatePublished - 1982

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