A multivariate “inv” hook formula for forests
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Björner and Wachs provided two q-generalizations of Knuth’s hook formula counting linear extensions of forests: one involving the major index statistic, and one involving the inversion number statistic. We prove a multivariate generalization of their inversion number result, motivated by specializations related to the modular invariant theory of finite general linear groups.
KeywordsHook formula Forests Moulds Binary search Free quasisymmetric functions Loday–Ronco algebra
Mathematics Subject Classification05A15 05A10
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