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Partial semigroups and primality indicators in the fractal generation of binomial coefficients to a prime square modulus

100%

Doan D. , Kivunge B. , Smith J. , Sykes T. , Teplitskiy M.

tom Vol. 42, nr 1

23-39

This paper, resulting from two summer programs of Research Experience for Undergraduates, examines the congruence classes of binomial coefficients to a prime square modulus as given by a fractal generation process for lattice path counts. The process depends on the isomorphism of partial semigroup structures associated with each iteration. We also consider integrality properties of certain critical coefficients that arise in the generation process. Generalizing the application of these coefficients to arbitrary arguments, instead of just to the prime arguments appearing in their original function, it transpires that integrality of the coefficients is indicative of the primality of the argument.

Harmonic sums and integral representations

67%

Sofo A.

tom Vol. 16, nr 2

265-277

In this paper we derive some identities of harmonic number sums with binomial coefficients, we also give integral representations for the sums. We recover some existing identities and introduce a number of new ones.