組合數學研討會
主講者: 1. 潘俊杰 教授 (輔仁大學數學系) 2. 鄭斯恩 教授 (國立高雄大學應數系)
講題: 1. Alon-Babai-Suzuki's Conjecture (2) 2. Some results about combinatorial statistics on non-crossing partitions
時間: 2014-12-26 (Fri.)  14:00 - 17:00
地點: 數學所 714 研討室 (台大院區)
Abstract: 1. In this talk, the speaker will talk about a new result of Kyung-Won Hwang and Younjin Kim on Alon-Babai-Suzuki's Conjecture. 2. Using two bijections, we give the most obvious $q$-analogue of the Narayana numbers based on non-crossing partitions. We also define two interesting decompositions of non-crossing partitions, and obtain recursions of joint distributions of statistics on non-crossing partitions. Using another bijection, we show that the statistic $2rs +n-bk$ on non-crossing partitions and the statistic $area$ on Dyck paths are equidistributed. Finally, we get an interesting $(q, x)$-refinement of the Catalan numbers through the connection between non-crossing partitions and $2$-Motzkin paths.
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