Nonnegativity results for generalized q-binomial coefficients

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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.

Original languageEnglish (US)
Pages (from-to)121-137
Number of pages17
JournalDiscrete Mathematics
Issue number1-3
StatePublished - Dec 16 1995
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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