Accessible Unlicensed Requires Authentication Published by De Gruyter November 5, 2010

On Ternary Inclusion-Exclusion Polynomials

Gennady Bachman
From the journal

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 Φpqr, where p < q < r are odd primes. Our main result is that the set of coefficients of Φpqr is simply a string of consecutive integers which depends only on the residue class of r modulo pq.

Received: 2009-12-12
Accepted: 2010-06-05
Published Online: 2010-11-05
Published in Print: 2010-November

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