Quantum integer-valued polynomials
Author(s)Harman, Nathan Reid; Hopkins, Sam
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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 N[q]. We then classify all maps from this ring into a field, extending a known classification in the classical case where q=1 .
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Journal of Algebraic Combinatorics
Harman, Nate, and Sam Hopkins. “Quantum Integer-Valued Polynomials.” Journal of Algebraic Combinatorics 45, no. 2 (October 4, 2016): 601–628.
Author's final manuscript