Nonnegativity results for generalized q-binomial coefficients

Susanna Fishel

doi:10.1016/0012-365X(94)00231-7

Nonnegativity results for generalized q-binomial coefficients

Susanna Fishel

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let q be a prime number. The number of subgroups of order q^k in an abelian group G of order qⁿ and type λ is a polynomial in q, [_k^λ′]_q. In 1987, Lynne Butler showed that the first difference, [_k^λ′] - [_{k - 1}^λ′], has nonnegative coefficients as a polynomial in q, when 2k ≤ |λ|. We generalize the first difference to the rth difference, and give conditions for the nonnegativity of its coefficients.

Original language	English (US)
Pages (from-to)	121-137
Number of pages	17
Journal	Discrete Mathematics
Volume	147
Issue number	1-3
DOIs	https://doi.org/10.1016/0012-365X(94)00231-7
State	Published - Dec 16 1995
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(94)00231-7

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abstract = "Let q be a prime number. The number of subgroups of order qk in an abelian group G of order qn and type λ is a polynomial in q, [kλ′]q. In 1987, Lynne Butler showed that the first difference, [kλ′] - [k - 1λ′], has nonnegative coefficients as a polynomial in q, when 2k ≤ |λ|. We generalize the first difference to the rth difference, and give conditions for the nonnegativity of its coefficients.",

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AB - Let q be a prime number. The number of subgroups of order qk in an abelian group G of order qn and type λ is a polynomial in q, [kλ′]q. In 1987, Lynne Butler showed that the first difference, [kλ′] - [k - 1λ′], has nonnegative coefficients as a polynomial in q, when 2k ≤ |λ|. We generalize the first difference to the rth difference, and give conditions for the nonnegativity of its coefficients.

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Nonnegativity results for generalized q-binomial coefficients

Abstract

ASJC Scopus subject areas

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