Contents

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Power compositions and semi-Pell compositions

William J. Keith1, Augustine O. Munagi2
1Department of Mathematical Sciences, Michigan Technological Universit
2 School of Mathematics, University of the Witwatersrand, Johannesburg

Abstract

In analogy with the semi-Fibonacci partitions studied recently by Andrews, we define semi-m-Pell compositions. We find that these are in bijection with certain weakly unimodal m-ary compositions. We give generating functions, bijective proofs, and a number of unexpected congruences for these objects. In the special case of m=2, we have a new combinatorial interpretation of the semi-Pell sequence and connections to other objects.