报告人：傅士硕

时 间：2026月10日25日 14:00

地 点：L-2620

报告摘要：Seeking to bridge the structural divide between a permutation's cycle notation and its one-line notation, Berman and Tenner introduced a novel notion of permutation pattern known as the arrow pattern. Recently, Archer and Laudone initiated a systematic study of arrow pattern avoidance, leaving behind three intriguing conjectures. In this talk, we resolve all three conjectures. First, we enumerate all six subclasses of permutations that simultaneously avoid a classical pattern of length 3 and a fixed arrow pattern of length 3, thereby confirming the first two conjectures. Second, we settle the third conjecture (which involves a different arrow pattern) by providing two independent proofs. These proofs rely on a restriction of Biane's bijection to non-nesting involutions and Krattenthaler's bijection from 321-avoiding permutations to Dyck paths, respectively. One more real-rootedness result will be mentioned if time permits.

专家简介:傅士硕，重庆大学数学与统计学院研究员，博士生导师。2011 年博士毕业于宾夕法尼亚州立大学，2011-2012 年在韩国科学技术院（KAIST）从事博士后研究，2012 年以“百人计划”特聘研究员入职重庆大学。主要研究兴趣为组合数学中的整数分拆理论、排列统计量同分布问题以及组合序列的伽马非负性等。已在 J. Combin. Theory Ser. A, Adv. Appl. Math., SIAM Disc.Math., European J. Combin., Ramanujan J. 等期刊发表论文 30 余篇，获批国家自然科学基金两项。现任中国工业与应用数学学会图论组合及应用专业委员会副秘书长, 中国运筹学会图论组合学分会理事, 重庆市运筹学会常务理事。