3 research outputs found
Freeness of Hyperplane Arrangements between Boolean Arrangements and Weyl Arrangements of Type
Every subarrangement of Weyl arrangements of type is represented
by a signed graph. Edelman and Reiner characterized freeness of subarrangements
between type and type in terms of graphs. Recently,
Suyama and the authors characterized freeness for subarrangements containing
Boolean arrangements satisfying a certain condition. This article is a sequel
to the previous work. Namely, we give a complete characterization for freeness
of arrangements between Boolean arrangements and Weyl arrangements of type in terms of graphs.Comment: 15 page
Worpitzky-compatible subarrangements of braid arrangements and cocomparability graphs
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 , are known as the graphic
arrangements. We prove that the Worpitzky-compatible graphic arrangements are
characterized by cocomparability graphs. Our main result yields new formulas
for the chromatic and graphic Eulerian polynomials of cocomparability graphs.Comment: 11 pages, comments are welcome