The KOH terms and classes of unimodal N-modular diagrams

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We show how certain suitably modified N-modular diagrams of integer partitions provide a nice combinatorial interpretation for the general term of Zeilbergerʼs KOH identity. This identity is the reformulation of OʼHaraʼs 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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© 2011 Elsevier Inc. All rights reserved. Publisher’s version of record: https://doi.org/10.1016/j.jcta.2011.06.010

Publication Title

Journal of Combinatorial Theory, Series A