报告时间：2022年12月12日 16：15开始
报 告 人：Simone Costa (University of Brescia)
报告地点：腾讯会议号460-404-932
报告题目：Bounds on the Higher Degree Erdős-Ginzburg-Ziv Constants over F_q^n
报告摘要：The classical Erdős-Ginzburg-Ziv constant of a group G denotes the smallest positive integer l such that any sequence S of length at least l contains a zero-sum subsequence of length |G|. In the recent paper, Caro and Schmitt generalized this concept, using the m-th degree symmetric polynomial e_m(S) instead of the sum of the elements of S and considering subsequences of a given length t. In particular, they defined the higher degree Erdős-Ginzburg-Ziv constants EGZ(t,R,m) of a finite commutative ring R and presented several lower and upper bounds to these constants. In this talk we will provide lower and upper bounds for EGZ(t,R,m) in case R=F_q^n. The lower bounds here presented have been obtained, respectively, using Lovász Local Lemma and the Expurgation method and, for sufficiently large n, they beat the lower bound provided by Caro and Schmitt for the same kind of rings. Finally, we will show an upper bound derived from Tao's Slice Rank method assuming that q=3^k with k>1, t=3, and m=2. (Joint work with Stefano Della Fiore)
报告人简介：Simone Costa received the M.S. degree (cum laude) in mathematics from the Catholic University of Milan in 2012 and the Ph.D. degree in mathematics from the University of Rome III in 2016 under the supervision of Professor Marco Buratti. He is currently an Assistant Professor (RTDB) with the Department of DICATAM, Mathematics Section, University of Brescia. His main research interests are in design theory, coding theory, graph-embeddings, combinatorial number theory, and extremal combinatorics.
