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

2013/02/08 by Masao Ishikawa, Ishikawa, Masao
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Mathematical functions and polynomials #math.CO

paper · pdf · doi:10.48550/arxiv.1302.1968

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

arxiv created 2013/02/08 · arxiv updated 2013/02/11

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 ₁₂W₁₁.

Citations

• (q,t)-deformations of multivariate hook product formulae
• Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture
• Bisymmetric functions, Macdonald polynomials and sl₃ basic hypergeometric series
• A Selberg integral for the Lie algebra A_n

Related

• A generalization of RSK to d-complete posets
• Hook length property of d-complete posets via q-integrals
• Counting linear extensions of posets with determinants of hook lengths
• The weighted hook length formula III: Shifted tableaux
• (q,t)-deformations of multivariate hook product formulae