The Degree of a $q$-Holonomic Sequence is a Quadratic Quasi-Polynomial

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The Degree of a q-Holonomic Sequence is a Quadratic Quasi-Polynomial

A sequence of rational functions in a variable q is q-holonomic if it satisfies a linear recursion with coefficients polynomials in q and qn. We prove that the degree of a q-holonomic sequence is eventually a quadratic quasi-polynomial, and that the leading term satisfies a linear recursion relation with constant coefficients. Our proof uses differential Galois theory (adapting proofs regarding...

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ژورنال

عنوان ژورنال: The Electronic Journal of Combinatorics

سال: 2011

ISSN: 1077-8926

DOI: 10.37236/2000