Reciprocals of subsum polynomials

The Ramanujan Journal, vol. 70

Abstract

Abstract We introduce the subsum polynomial of a partition $$\lambda =(\lambda _1, \lambda _2, \ldots , \lambda _k)$$ λ = ( λ 1 , λ 2 , … , λ k ) defined by $$\textrm{sp}(\lambda , x)=\prod _{i=1}^k(1+x^{\lambda _i})$$ sp ( λ , x ) = ∏ i = 1 k ( 1 + x λ i ) . We study the sum of reciprocals of $$\textrm{sp}(\lambda , x)$$ sp ( λ , x ) over all partitions of n . We prove arithmetic properties of related polynomials and offer connections to other combinatorial objects.

Authors 4

1. Cristina Ballantine

   College of the Holy Cross

   Affiliation as printed

   Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, MA, 01610, USA

2. George Beck

   Dalhousie University

   Affiliation as printed

   Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 4R2, Canada

3. Brooke Feigon

   City College of New York

   Affiliation as printed

   Department of Mathematics, The City College of New York, CUNY, New York, NY, 10031, USA

4. Kathrin Maurischat corresponding Aachen Fachgruppe Mathematik

   RWTH Aachen University

   Affiliation as printed

   Fachgruppe Mathematik, RWTH Aachen University, Pontdriesch 12-16, 52056, Aachen, Germany