Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zeilberger's KOH theorem and the strict unimodality of q-binomial
  coefficients   A recent nice result due to I. Pak and G. Panova is the strict unimodality of
the $q$-binomial coefficients $\binom{a+b}{b}_q$ (see \cite{PP} and also
\cite{PP2} for a slightly revised version of their theorem). Since their proof
used representation theory and Kronecker coefficients, the authors also asked
for an argument that would employ Zeilberger's KOH theorem. In this note, we
give such a proof. Then, as a further application of our method, we also
provide a short proof of their conjecture that the difference between
consecutive coefficients of $\binom{a+b}{b}_q$ can get arbitrarily large, when
we assume that $b$ is fixed and $a$ is large enough.

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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg