Quantum integer-valued polynomials

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• 作者：Nate Harman ; Sam Hopkins
• 关键词：q ; analogs ; Integer ; valued polynomials ; Quantum integers ; Combinatorial identities
• 刊名：Journal of Algebraic Combinatorics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：45
• 期：2
• 页码：601-628
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Combinatorics; Convex and Discrete Geometry; Order, Lattices, Ordered Algebraic Structures; Computer Science, general; Group Theory and Generalizations;
• 出版者：Springer US
• ISSN：1572-9192
• 卷排序：45

文摘

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 \(q=1\).