Polynomial analogues of Ramanujan congruences for Han's hooklength formula

• Autorzy: William J. Keith
• Języki publikacji: EN

Abstrakty

EN

This article considers the eta power $∏_{(1-q^k)}^{b-1}$. It is proved that the coefficients of ${q^n/n!}$ in this expression, as polynomials in b, exhibit equidistribution of the coefficients in the nonzero residue classes mod 5 when n = 5j+4. Other symmetries, as well as symmetries for other primes and prime powers, are proved, and some open questions are raised.

Kategorie tematyczne

• 05A17: Partitions of integers
• 05A10: Factorials, binomial coefficients, combinatorial functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 160
• Numer: 4
• Strony: 303-315

Daty

wydano

2013

Twórcy

autor

William J. Keith

• Michigan Technological University, Fisher Hall 319, 1400 Townsend Drive, Houghton, MI 49931, U.S.A.

Identyfikatory

DOI

10.4064/aa160-4-1