Speaker : Professor Jiang Zeng (Universite Claude Bernard Lyon-I )
Title : Some positivity problems in combinatorics via continued fractions
Time : 2018-02-09 (Fri) 15:00 - 16:00
Place : Auditorium, 6 Floor, Institute of Mathematics (NTU Campus)
Abstract: Many well-known sequences in combinatorics are unimodal or log-concave, sometimes they are also $\gamma$-positive. After a review of background, we present the continued fraction approach. We then present Stieltjes-type and Jacobi-type continued fractions for some "master polynomials" that enumerate permutations, set partitions or perfect matchings with a large (some infinite) number of simultaneous statistics. Our results contain many previously obtained identities as special cases, providing a common refinement of all of them.