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On Pascal's triangle modulo $p^2$

100%

Huard J. G. , Spearman B. K. , Williams K. S.

nr 1

157-165

Jordan numbers, Stirling numbers and sums of powers

44%

Wituła R. , Kaczmarek K. , Lorenc P. , Hetmaniok E. , Pleszczyński M.

nr 2

155-166

In the paper a new combinatorical interpretation of the Jordan numbers is presented. Binomial type formulae connecting both kinds of numbers mentioned in the title are given. The decomposition of the product of polynomial of variable n into the sums of kth powers of consecutive integers from 1 to n is also studied.

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

38%

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

26%

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.