学术活动

报告题目：The size and structure of maximal d-wise intersecting families and cross-intersecting families

主讲人：张孟龙

报告时间：10月19日 11:20-11:50

报告地点：西安电子科技大学南校区会议中心B101报告厅

For a positive integer , a family  is said to be -wise intersecting if for all . A -wise intersecting family is called maximal if is not -wise intersecting for any . This talk provides a refinement of O'Neill and Verstraëte's results about the structure of the largest and the second largest maximal non-trivial -wise intersecting -uniform families. This talk also determines the structure of the third largest and the fourth largest maximal non-trivial -wise intersecting -uniform families for any , and the fifth largest and the sixth largest maximal non-trivial 3-wise intersecting -uniform families for any , in the asymptotic sense.

The families are said to be cross-intersecting if for any and , . Cross-intersecting families are said to be non-empty if for any . This talk shows that if are non-empty cross-intersecting families with  and , then .

This solves a problem posed by Shi, Frankl and Qian. The extremal families attaining the upper bounds are also characterized.

张孟龙，西安电子科技大学博士后，合作导师为葛根年教授。2024年博士毕业于北京交通大学，导师为冯弢教授。主要从事组合设计、编码理论与极值组合的研究。近五年来，相关论文发表至组合学领域重要期刊《Journal of Combinatorial Theory, Series A》、《European Journal of Combinatorics 》、《Discrete Mathematics 》和《 Journal of Combinatorial Designs》以及编码密码学三大期刊之一的《Designs,Codes and Cryptography》。共发表论文7篇，其中关于极大d-wise相交族结构的文章被《Discrete Mathematics》期刊编委会评选为2023年该刊杰出论文。