5 papers
Expectations of Tutte-related functions of random ranked sets with multiplicities
Tan Nhat Tran
Employing two models, we show that various counting functions of a random variable defined by restriction or contraction of a ranked set with multiplicity (e.g., classical and arit…
Eulerian polynomials for subarrangements of Weyl arrangements
Ahmed Umer Ashraf, Tan Nhat Tran, Masahiko Yoshinaga
Let be a Weyl arrangement. We introduce and study the notion of -Eulerian polynomial producing an Eulerian-like polynomial for any subarrangement of $\ma…
On restrictions of Weyl arrangements
Takuro Abe, Hiroaki Terao, Tan Nhat Tran
Let be a Weyl arrangement in an -dimensional Euclidean space. The freeness of restrictions of was first settled by a case-by-case method by Orlik…
Combinatorics of certain abelian Lie group arrangements and chromatic quasi-polynomials
Tan Nhat Tran, Masahiko Yoshinaga
The purpose of this paper is twofold. Firstly, we generalize the notion of characteristic polynomials of hyperplane and toric arrangements to those of certain abelian Lie group arr…
Characteristic quasi-polynomials of ideals and signed graphs of classical root systems
Tan Nhat Tran
With a main tool is signed graphs, we give a full description of the characteristic quasi-polynomials of ideals of classical root systems () with respect to the integer and r…