An identity arising in 3-noncrossing partitions

par Zhicong Lin (NIMS, Daejeon, Corée du Sud)

mardi 21 mars 2017, 10:45 → 11:45 Europe/Paris

Bât. Braconnier, salle Fokko du Cloux (ICJ, Université Lyon 1)

We prove a conjecture due independently to Yan and Martinez-Savage that asserts inversion sequences with no weakly decreasing subsequence of length 3 and enhanced 3-noncrossing partitions have the same cardinality. Our approach applies both West's generating tree technique and the so-called obstinate kernel method developed by Bousquet-Mélou. One application of this equinumerosity is a discovery of an intriguing identity involving numbers of classical and enhanced 3-noncrossing partitions.