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arXiv · 1712.07483

Weighted Lattice Paths Enumeration by Gaussian Polynomials

Ivica Martinjak·Ivana Zubac
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Abstract

The Gaussian polynomial in variable $q$ is defined as the $q$-analog of the binomial coefficient. In addition to remarkable implications of these polynomials to abstract algebra, matrix theory and quantum computing, there is also a combinatorial interpretation through weighted lattice paths. This interpretation is equivalent to weighted board tilings, which can be used to establish Gaussian polynomial identities. In particular, we prove duals of such identities and evaluate related sums.

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Ivica Martinjak, Ivana Zubac. 2017-12-20. Weighted Lattice Paths Enumeration by Gaussian Polynomials. https://doi.org/10.5592/co%2Fccd.2016.04

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