On a Class of Ternary Inclusion-Exclusion Polynomials
-
Gennady Bachman
and
Pieter Moree
Abstract
A ternary inclusion-exclusion polynomial is a polynomial of the form
where p, q, and r are integers ≥ 3 and relatively prime in pairs. This class of polynomials contains, as its principle subclass, the ternary cyclotomic polynomials corresponding to restricting p, q, and r to be distinct odd prime numbers. Our object here is to continue the investigation of the relationship between the coefficients of Q{p,q,r} and Q{p,q,s}, with r ≡ s (mod pq). More specifically, we consider the case where 1 ≤ s < max(p, q) < r, and obtain a recursive estimate for the function A(p, q, r) – the function that gives the maximum of the absolute values of the coefficients of Q{p,q,r}. A simple corollary of our main result is the following absolute estimate. If s ≥ 1 and r ≡ ±s (mod pq), then A(p, q, r) ≤ s.
© de Gruyter 2011
Articles in the same Issue
- Symmetries in Steinhaus Triangles and in Generalized Pascal Triangles
- Unbounded Discrepancy in Frobenius Numbers
- Combinatorial Interpretations of Convolutions of the Catalan Numbers
- Quadratic Forms and Four Partition Functions Modulo 3
- On Bases with a T-Order
- Van der Waerden's Theorem and Avoidability in Words
- On a Class of Ternary Inclusion-Exclusion Polynomials
Articles in the same Issue
- Symmetries in Steinhaus Triangles and in Generalized Pascal Triangles
- Unbounded Discrepancy in Frobenius Numbers
- Combinatorial Interpretations of Convolutions of the Catalan Numbers
- Quadratic Forms and Four Partition Functions Modulo 3
- On Bases with a T-Order
- Van der Waerden's Theorem and Avoidability in Words
- On a Class of Ternary Inclusion-Exclusion Polynomials
