# Registered Data

## [00598] Hyperplane arrangements and enumerative problems

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Proposal of Minisymposium**Abstract**: Hyperplane arrangements appear in many areas of mathematics, including topology, combinatorics, algebraic geometry. One of the important aspects is that hyperplane arrangements have several discrete structures e.g., poset of intersections, chambers, lattice points. Enumerations of these objects play crucial roles in many problems, e.g., enumerative problems, coding theory. In this minisymposium, we focus on enumerative aspects of these objects.**Organizer(s)**: Masahiko Yoshinaga, Norihiro Nakashima**Classification**:__52C35__,__05C31__**Speakers Info**:- Tsuyoshi Miezaki (Waseda University)
- Norihiro Nakashima (Nagoya Institute of Technology)
- Yasuhide Numata (Hokkaido University)
- Shuhei Tsujie (Hokkaido University of Education)

**Talks in Minisymposium**:**[01780] Counting the regions of hyperplane arrangements related to Coxeter arrangements.****Author(s)**:**Yasuhide Numata**(Hokkaido University)

**Abstract**: We consider the Shi and Ish arrangement of type $B_n$. Both are hyperplane arrangements in the real vector space of dimension $n$ containing the Coxeter arrangement of type $B_n$. We discuss combinatorial objects which parametrize the regions, i.e. connected components of complement of the arrangement, of these arrangement.

**[01791] Characteristic quasi-polynomials of arrangements over algebraic integers****Author(s)**:**Shuhei Tsujie**(Hokkaido University of Education)

**Abstract**: Kamiya, Takemura, and Terao initiated the theory of the characteristic quasi-polynomial of an integral arrangement, which is a function counting the elements in the complement of the arrangement modulo positive integers. In this talk, we will discuss arrangements over the rings of integers of algebraic number fields.

**[01887] Coboundary polynomial and related polynomial invariants****Author(s)**:**Norihiro Nakashima**(Nagoya Institute of Technology)

**Abstract**: The coboundary polynomial is a polynomial computed by all characteristic polynomials for restriction arrangements to all flats in the intersection poset. It is known that the coboundary polynomial is essentially the same as the weight enumerator and Tutte polynomial. In this talk, we introduce some known results about these relationship and future issues.

**[01889] Generalizations of Tutte-Grothendieck polynomials****Author(s)**:**Tsuyoshi Miezaki**(Waseda University)- HIMADRI SHEKHAR CHAKRABORTY (Shahjalal University of Science and Technology)
- CHONG ZHENG (Waseda University)

**Abstract**: A Tutte-Grothendieck polynomial is a graph invariant that satisfies a generalized deletion-contraction formula. In this talk, we introduce the notion of weighted Tutte-Grothendieck polynomial and weighted Tutte-Grothendieck invariant for matroid and discuss some of its properties. Moreover, we show that the weighted Tutte-Grothendieck invariant is stronger than the Tutte-Grothendieck invariant. This is joint work with Himadri Chakraborty (SUST) and Chong Zheng (Waseda University).