Time: 9h30 Tuesday, August 18, 2026-

Room 612 - A6 - Institute of Mathematics, 18 Hoang Quoc Viet.

Abstract. Many combinatorial structures arising in different areas of mathematics exhibit striking similarities, suggesting the existence of a common underlying principle. In this talk, I will present a framework that unifies several seemingly unrelated objects, including MAT-labeled graphs from the theory of hyperplane arrangements, regular vines from probability theory, and maximal Arrow’s single-peaked domains from social choice theory.

The key idea is an axiomatic recursive construction based on two simple operations, called splitting and merging, which completely characterizes all of these objects. This viewpoint leads to explicit correspondences between them and provides new combinatorial and axiomatic characterizations of maximal single-peaked domains.

The talk requires only elementary linear algebra and basic combinatorics, and no background in hyperplane arrangements, probability, or social choice theory will be assumed. If time permits, I will also explain how the same framework naturally extends to extremal lattices from formal concept analysis and extremal binary matrices with no triangles from combinatorial matrix theory.

The talk is based on recent joint work with H. M. Tran (Hanoi) and S. Tsujie (Hokkaido).