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Tri-Restricted Numbers and Powers of Permutation Representations

Ji Young Choi1, Jonathan D.H.Smith1
1Department Of Mathematics, Iowa State University, Ames, Ia 50011, USA

Abstract

Let G be a transitive permutation group on a set Q. The orbit decompositions of the actions of G on the sets of ordered n-tuples with elements repeated at most three times are studied. The decompositions involve Stirling numbers and a new class of related numbers, the so-called tri-restricted numbers. The paper presents exponential generating functions for the numbers of orbits, and examines relationships between various powers of the G-set involving Stirling numbers, the tri-restricted numbers, and the coefficients of Bessel polynomials.

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