On Ternary Inclusion-Exclusion Polynomials

2010/06/02 by Gennady Bachman, Bachman, Gennady
Mathematics · #11B83 #11C08 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B83 #msc:11C08

paper · pdf · doi:10.48550/arxiv.1006.0518

12 pages; final version-to appear in Integers

arxiv created 2010/06/02 · arxiv updated 2010/06/04

Abstract

Taking a combinatorial point of view on cyclotomic polynomials leads to a larger class of polynomials we shall call the inclusion-exclusion polynomials. This gives a more appropriate setting for certain types of questions about the coefficients of these polynomials. After establishing some basic properties of inclusion-exclusion polynomials we turn to a detailed study of the structure of ternary inclusion-exclusion polynomials. The latter subclass is exemplified by cyclotomic polynomials Φ_pqr, where p<q<r are odd primes. Our main result is that the set of coefficients of Φ_pqr is simply a string of consecutive integers which depends only on the residue class of r modulo pq.

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