The KOH terms and classes of unimodal N-modular diagrams

Details The KOH terms and classes of unimodal N-modular diagrams The KOH terms and classes of unimodal N-modular diagrams

2011-01-07

arxiv.org/abs/1101.1475v2

J. Combin. Theory Ser. A 118 (2011), no. 8, 2498-2510

Mathematics

Combinatorics

Several mostly minor or notational changes with respect to the first version, in response to the referees' comments. 13 pages,

Scientific paper

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.

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