We define and study odd analogues of classical geometric and combinatorial objects associated to permutations, namely odd Schubert varieties, odd diagrams, and odd inversion sets. We show that there is a bijection between odd inversion sets of permutations and acyclic orientations of the Turán graph, that the dimension of the odd Schubert variety associated to a permutation is the odd length of the permutation, and give several necessary conditions for a subset of [ n ] × [ n ] to be the odd diagram of a permutation. We also study the sign-twisted generating function of the odd length over descent classes of the symmetric groups.

Brenti, F., Carnevale, A. (2021). Odd length: odd diagrams and descent classes. DISCRETE MATHEMATICS, 344(5) [10.1016/j.disc.2021.112308].

Odd length: odd diagrams and descent classes

Brenti F.
;
2021-01-01

Abstract

We define and study odd analogues of classical geometric and combinatorial objects associated to permutations, namely odd Schubert varieties, odd diagrams, and odd inversion sets. We show that there is a bijection between odd inversion sets of permutations and acyclic orientations of the Turán graph, that the dimension of the odd Schubert variety associated to a permutation is the odd length of the permutation, and give several necessary conditions for a subset of [ n ] × [ n ] to be the odd diagram of a permutation. We also study the sign-twisted generating function of the odd length over descent classes of the symmetric groups.
2021
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/02 - ALGEBRA
English
Con Impact Factor ISI
Permutation; Generating function; Descent class; Diagram; Odd length; Schubert variety
https://www.sciencedirect.com/science/article/pii/S0012365X21000212/pdfft?md5=958ae00705d0b25c8eb32ed7efdd6f42&pid=1-s2.0-S0012365X21000212-main.pdf
https://www.mat.uniroma2.it/~brenti/60.pdf
Brenti, F., Carnevale, A. (2021). Odd length: odd diagrams and descent classes. DISCRETE MATHEMATICS, 344(5) [10.1016/j.disc.2021.112308].
Brenti, F; Carnevale, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/287489
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