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arXiv · 1601.06110

Quantum integer-valued polynomials

Nate Harman·Sam Hopkins
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Abstract

We define a $q$-deformation of the classical ring of integer-valued polynomials which we call the ring of quantum integer-valued polynomials. We show that this ring has a remarkable combinatorial structure and enjoys many positivity properties: for instance, the structure constants for this ring with respect to its basis of $q$-binomial coefficient polynomials belong to $\mathbb{N}[q]$. We then classify all maps from this ring into a field, extending a known classification in the classical case where $q=1$.

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Nate Harman, Sam Hopkins. 2016-01-22. Quantum integer-valued polynomials. https://doi.org/10.1007/s10801-016-0717-3

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