Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
林志聪, 集美大学数学系
Inviter:
陈绍示
Title:
Restricted inversion sequences and enhanced $3$-noncrossing partitions
Time & Venue:
2018.7.5 16:00-17:00 N205
Abstract
Yan and Martinez--Savage conjectured independently that inversion sequences with no weakly decreasing subsequence of length $3$ and enhanced $3$-noncrossing partitions have the same cardinality. In this talk, I will present an algebraic proof, which applies both the generating tree technique and the so-called obstinate kernel method developed by Bousquet-M\'elou. As one application of this equinumerosity, an intriguing identity involving numbers of classical and enhanced $3$-noncrossing partitions was discovered.I will also pose a related functional equation, enumerating another interesting class of restricted inversion sequences, that I could not solve.