Hook formulas for skew shapes. IV: Increasing tableaux and factorial Grothendieck polynomials. (English) Zbl 1491.05193
J. Math. Sci., New York 261, No. 5, 630-657 (2022) and Zap. Nauchn. Semin. POMI 507, 59-98 (2021).
Summary: We present a new family of hook-length formulas for the number of standard increasing tableaux which arise in the study of factorial Grothendieck polynomials. In the case of straight shapes, our formulas generalize the classical hook-length formula and the Littlewood formula. For skew shapes, our formulas generalize the Naruse hook-length formula and its \(q\)-analogs, which were studied in previous papers of the series.
For Part III see [the authors, Algebr. Comb. 2, No. 5, 815–861 (2019; Zbl 1425.05158)].
For Part III see [the authors, Algebr. Comb. 2, No. 5, 815–861 (2019; Zbl 1425.05158)].
MSC:
| 05E10 | Combinatorial aspects of representation theory |
| 05A05 | Permutations, words, matrices |
| 14M15 | Grassmannians, Schubert varieties, flag manifolds |
Citations:
Zbl 1425.05158Software:
OEISOnline Encyclopedia of Integer Sequences:
Square array of Delannoy numbers D(i,j) (i >= 0, j >= 0) read by antidiagonals.References:
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