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.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics