arXiv 1302.19682013-02-08math.CO

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

Masao Ishikawa

备注：: 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

英文摘要：

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 ${}_{12}W_{11}$.

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