✦ LIBER ✦

Nonnegativity results for generalized q-binomial coefficients

✍ Scribed by Susanna Fishel

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 585 KB
Volume: 147
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00231-7

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✦ Synopsis

Let q be a prime number. The number of subgroups of order qk in an abelian group G of order qn and type 2 is a polynomial in q, [ak']~. In 1987, Lynne Butler showed that the first difference, I-~,'] -[ka-'~], has nonnegative coefficients as a polynomial in q, when 2k ~< 12[. We generalize the first difference to the rth difference, and give conditions for the nonnegativity of its coefficients.

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