(q,t)-hook formula for Birds and Banners

Abstract

We study Okada's conjecture on $(q,t)$-hook formula of general $d$-complete posets. Proctor classified $d$-complete posets into 15 irreducible ones. We try to give a case-by-case proof of Okada's $(q,t)$-hook formula conjecture using the symmetric functions. Here we give a proof of the conjecture for birds and banners, in which we use Gasper's identity for VWP-series ${}_{12}{W}_{11}$.

27 pages, 7 figures. arXiv admin note: text overlap with arXiv:0909.0086, arXiv:0905.4033, arXiv:math/0511333, arXiv:0708.1193 by other authors

References in corpus (4)

• Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture
• Shifted Schur process and asymptotics of large random strict plane partitions
• Rogers-Szego polynomials and Hall-Littlewood symmetric functions
• A generalization of MacMahon's formula