The KOH terms and classes of unimodal N-modular diagrams

Authors:
Fabrizio Zanello
Affiliations:
Department of Mathematics, MIT, Cambridge, MA 02139-4307, United States and Department of Mathematical Sciences, Michigan Tech, Houghton, MI 49931-1295, United States
Venue:
Journal of Combinatorial Theory Series A
Year:
2011

Citing 4
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Abstract

We show how certain suitably modified N-modular diagrams of integer partitions provide a nice combinatorial interpretation for the general term of Zeilberger@?s KOH identity. This identity is the reformulation of O@?Hara@?s famous proof of the unimodality of the Gaussian polynomial as a combinatorial identity. In particular, we determine, using different bijections, two main natural classes of modular diagrams of partitions with bounded parts and length, having the KOH terms as their generating functions. One of our results greatly extends recent theorems of J. Quinn et al., which presented striking applications to quantum physics.