题目：Transitive and Gallai colorings
报告人：李建荣(维也纳大学)
时间：2024年2月4日上午8：30—11：30
地 点：学院楼413
摘要:A Gallai coloring of the complete graph is an edge-coloring with no rainbow triangle. This concept first appeared in the study of comparability graphs and anti-Ramsey theory. In this talk, I will talk about a recent joint work with Ron M. Adin, Arkady Berenstein, Jacob Greenstein, Avichai Marmor, Yuval Roichman, in which we introduce a transitive analogue for acyclic directed graphs, and generalize both notions to Coxeter systems, matroids and commutative algebras. We show that for any finite matroid (or oriented matroid), the maximal number of colors is equal to the matroid rank. This generalizes a result of Erdős-Simonovits-Sós for complete graphs. We prove that the number of Gallai (or transitive) colorings of the matroid that use at most k colors is a polynomial in k. We count Gallai and transitive colorings of the root system of type A using the maximal number of colors, and show that, when equipped with a natural descent set map, the resulting quasisymmetric function is symmetric and Schur-positive.
报告人简介：李建荣，2012年博士毕业于兰州大学数学与统计学院并留校工作，现为维也纳大学博士后研究员，从事量子群，表示论，丛代数，数学物理等研究。现主持完成国家自然基金青年项目1项，主持完成奥地利自然科学基金1项，主持在研奥地利自然科学基金1项。在Selecta Mathematica,Mathematische Zeitschrift, Int. Math.Res. Notices, J. Algebra, Algeb. Rep. Theory, J. AlgebraicComb., J. Lie theory等国际SCI期刊上发表学术论文20余篇。
