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math.CO2022
An application of sums of triple products of binomials
Michael J. J. Barry
We prove that a certain family of sums of products of three binomials has alternating behavior modulo a prime . To accomplish this we rewrite these sums as signed sums of produc…
math.CO2020
Set Equality in Combinatorial Game Theory
Michael J. J. Barry
In Combinatorial Game Theory, the fundamental relation of game equivalence, denoted by , is introduced early on and overrides the notion of set equality. We explore what happens…