A multivariate "inv" hook formula for forests

Florent Hivert; Victor Reiner

doi:10.1007/s11139-012-9390-x

A multivariate "inv" hook formula for forests

Florent Hivert, Victor Reiner

School of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	33-51
Number of pages	19
Journal	Ramanujan Journal
Volume	31
Issue number	1-2
DOIs	https://doi.org/10.1007/s11139-012-9390-x
State	Published - Jun 2013

Bibliographical note

Funding Information:
First author partially supported by grant ANR-06-BLAN-0380. Second author partially supported by NSF grant DMS-0601010.

Keywords

Binary search
Forests
Free quasisymmetric functions
Hook formula
Loday-Ronco algebra
Moulds

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10.1007/s11139-012-9390-x

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abstract = "Bj{\"o}rner 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.",

keywords = "Binary search, Forests, Free quasisymmetric functions, Hook formula, Loday-Ronco algebra, Moulds",

author = "Florent Hivert and Victor Reiner",

note = "Funding Information: First author partially supported by grant ANR-06-BLAN-0380. Second author partially supported by NSF grant DMS-0601010.",

year = "2013",

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language = "English (US)",

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AU - Hivert, Florent

AU - Reiner, Victor

N1 - Funding Information: First author partially supported by grant ANR-06-BLAN-0380. Second author partially supported by NSF grant DMS-0601010.

PY - 2013/6

Y1 - 2013/6

N2 - 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.

AB - 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.

KW - Binary search

KW - Forests

KW - Free quasisymmetric functions

KW - Hook formula

KW - Loday-Ronco algebra

KW - Moulds

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JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 1-2

ER -

A multivariate "inv" hook formula for forests

Abstract

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