Worpitzky-compatible subarrangements of braid arrangements and cocomparability graphs

Tan Nhat Tran; Akiyoshi Tsuchiya

doi:10.5802/crmath.210

Combinatoire

Worpitzky-compatible subarrangements of braid arrangements and cocomparability graphs

Tan Nhat Tran ¹ ; Akiyoshi Tsuchiya ²

¹ Tan Nhat Tran, Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo 060-0810, Japan
² Akiyoshi Tsuchiya, Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan

Comptes Rendus. Mathématique, Volume 359 (2021) no. 6, pp. 665-674.

Résumé

The class of Worpitzky-compatible subarrangements of a Weyl arrangement together with an associated Eulerian polynomial was recently introduced by Ashraf, Yoshinaga and the first author, which brings the characteristic and Ehrhart quasi-polynomials into one formula. The subarrangements of the braid arrangement, the Weyl arrangement of type $A$ , are known as the graphic arrangements. We prove that the Worpitzky-compatible graphic arrangements are characterized by cocomparability graphs. This can be regarded as a counterpart of the characterization by Stanley and Edelman–Reiner of free and supersolvable graphic arrangements in terms of chordal graphs. Our main result yields new formulas for the chromatic and graphic Eulerian polynomials of cocomparability graphs.

Reçu le : 2021-01-29
Accepté le : 2021-04-05
Publié le : 2021-08-25

DOI : 10.5802/crmath.210

Classification : 05C75, 17B22, 52C35, 05C31

Affiliations des auteurs :

Tan Nhat Tran ¹ ; Akiyoshi Tsuchiya ²

¹ Tan Nhat Tran, Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo 060-0810, Japan
² Akiyoshi Tsuchiya, Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Worpitzky-compatible subarrangements of braid arrangements and cocomparability graphs},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {665--674},
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     volume = {359},
     number = {6},
     year = {2021},
     doi = {10.5802/crmath.210},
     language = {en},
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Tan Nhat Tran; Akiyoshi Tsuchiya. Worpitzky-compatible subarrangements of braid arrangements and cocomparability graphs. Comptes Rendus. Mathématique, Volume 359 (2021) no. 6, pp. 665-674. doi : 10.5802/crmath.210. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.210/

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