The KOH terms and classes of unimodal N-modular diagrams
Document Type
Article
Publication Date
11-2011
Abstract
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.
Publication Title
Journal of Combinatorial Theory, Series A
Recommended Citation
Zanello, F.
(2011).
The KOH terms and classes of unimodal N-modular diagrams.
Journal of Combinatorial Theory, Series A,
118(8), 2498-2510.
http://doi.org/10.1016/j.jcta.2011.06.010
Retrieved from: https://digitalcommons.mtu.edu/math-fp/48
Publisher's Statement
© 2011 Elsevier Inc. All rights reserved. Publisher’s version of record: https://doi.org/10.1016/j.jcta.2011.06.010