报告题目：The Hecke Insertion Algorithm and Two Combinatorial Problems

报告人：陈永川院士 天津大学应用数学中心

时间：5月10号 16:00

地点：管研楼1518

摘要：The Hecke insertion algorithm was developed by Buch, Kresch,Shimozono,Tamvakis and Yong [Math. Ann., 2008] in order to expand a stableGrothendieckpolynomial in terms of stable Grothendieck polynomials indexed byinteger parti-tions. The notion of a rook strip was introduced by Buch [ActaMath., 2002] inthe study of the Littlewood-Richardson rule for stableGrothendieck polynomials.We introduce the notion of Hecke diagrams and thestructure of vacillating Hecketableaux. A Hecke diagram is defined as a Youngdiagram possibly with a markedcorner. A vacillating Hecke tableaux is asequence of Hecke diagrams subject tocertain conditions on the addition anddeletion of rook strips. Using the Heckeinsertion algorithm, we establish aone-to-one correspondence between vacillatingHecke tableaux and linkedpartitions which arise in free probability theory. Basedon this correspondence,we show that the crossing number and the nesting numberhave a symmetric jointdistribution over linked partitions, confirming a conjec-ture of de Mier[Electron. J. Combin., 2006]. We also prove a conjecture of Kim[SIAM J.Discrete Math., 2011] which states that the crossing number and thenestingnumber have a symmetric joint distribution over the front representationsofpartitions.

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