JCCA 2016 mini-symposium
Enumerative Combinatorics

This mini-symposium on enumerative combinatorics is one of mini-symposia during the Japanese Conference on Combinatorics and its Applications in Kyoto.

All participants should make a registration of the main conference "the Japanese Conference on Combinatorics and its Applications". Please visit the page for registration to make registration.

Now we are arranging the schedule of talks.

2016 May 22nd (Sun) 15:00-18:00

15:00 - 15:30

HIGASHITANI, Akihiro (Kyoto Sangyo University)

Ehrhart polynomials of lattice simplices and linear binary code.

Ehrhart polynomials of lattice polytopes are the enumerative function counting the lattice points contained in the dilation of a given lattice polytope. In this talk, after introducing some elements of Ehrhart theory, we focus on the Ehrhart polynomials of lattice simplices and present some results on a relation between them and linear binary codes.

15:45 - 16:15

KIM, Jang Soo (Sungkyunkwan University)

On $q$-integrals over order polytopes.

In this talk we express a $q$-integral over an order polytope coming from a poset as a sum over all linear extensions of the poset. As an application, we give a combinatorial interpretation of a $q$-Selberg integral, which generalizes Stanley's combinatorial interpretation of the Selberg integral. This is joint work with Dennis Stanton.

16:30 - 17:00

KAMIOKA, Shuhei(Kyoto University)

Triple product formulae for boxed plane partitions derived from orthogonal polynomials.

A generalization of MacMahon's triple product formula for boxed plane partitions is derived by means of orthogonal polynomials. A combinatorial interpretation of orthogonal polynomials in terms of (non-intersecting) lattice paths directly connects orthogonal polynomials with plane partitions. The interpretation is used to derive from the little $q$-Laguerre polynomials a new triple product formula for plane partitions which generalizes MacMahon's triple product formula as well as the trace generating function by Stanley.

17:15 - 17:45

EU, Sen-Peng (National Taiwan Normal University & Chinese Air Force Academy)

Evacuation and cyclic sieving on partitions.

We investigate the evacuation operation over chains induced by a partition shape and obtain cyclic sieving results for certain shapes.

Organizers: Yasuhide Numata (Shinshu University, nu at math.shinshu-u.ac.jp) and Soichi Okada (Nagoya University).