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math.CO2026
New central -binomial identities
Shane Chern, Karl Dilcher, Lin Jiu
We establish several new series evaluations involving the central -binomial coefficients, with the inspiration coming from earlier work by Vignat and one of the authors on the l…
math.CO2025
Colored base-3 partitions, sequences of polynomials, and perfect numbers
Karl Dilcher, Larry Ericksen
Motivated by the observation that the counting function of a certain base-3 colored partition contains the even perfect numbers as a subsequence, we begin by defining a sequence of…
math.CO2024
Polynomials and algebraic curves related to certain binary and -ary overpartitions
Karl Dilcher, Larry Ericksen
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 s…