Polynomials and algebraic curves related to certain binary and b-ary overpartitions

2024/05/20 by Karl Dilcher, Dilcher, Karl, Larry Ericksen +1 · 1 citation
Mathematics · #Meromorphic and Entire Functions #Advanced Mathematical Identities #Advanced Mathematical Theories

paper · pdf · doi:10.48550/arxiv.2405.12024

Abstract

We begin by considering a sequence of polynomials in three variables whose coefficients count restricted binary overpartitions with certain properties. We then concentrate on two specific subsequences that are closely related to the Chebyshev polynomials of both kinds, deriving combinatorial and algebraic properties of some special cases. We show that the zeros of these polynomial sequences lie on certain algebraic curves, some of which we study in greater detail. Finally, we extend part of this work to restricted b-ary overpartitions for arbitrary integers b≥ 2.

Cited by

• Colored base-3 partitions, sequences of polynomials, and perfect numbers

Related

• Curves defined by Chebyshev polynomials
• Colored base-3 partitions, sequences of polynomials, and perfect numbers
• Algebraic functions with infinitely many values in a number field
• Generalizations of Chebyshev Polynomials and Polynomial Mappings
• Polynomial analogues of restricted multicolor b-ary partition functions