2022 Combinatorics Workshop

Session

Session 4

1 Oct 2022, 14:15

Description

Chair: Sejeong Bang

45. Chromatic quasisymmetric functions and linked rook placements

Seung Jin Lee (Seoul National University)

01/10/2022, 14:15

Invited talk

R. Stanley introduced the chromatic symmetric functions of a graph $G$. This definition was later refined by J. Shareshian and M. Wachs, where a parameter $q$ is introduced in the definition of chromatic uasisymmetric functions. In this talk, we discuss two separate results and their connection: (1) a Hall-Littlewood expansion of the chromatic quasisymmetric functions (2) $e$-positivity of the...

25. $(q,t)$-analogues of $n!$ and $(n+1)^{n-1}$

Jaeseong Oh (Korea Institute for Advanced Study)

01/10/2022, 15:15

Contributed talk

The numbers $n!$ and $(n+1)^{n-1}$ are ubiquitous in combinatorics. Each number counts number of permutations and parking functions, respectively. I will discuss their $(q,t)$-generalizations and further generalization to symmetric functions, namely the modified Macdonald polynomials $\widetilde{H}_\mu$ and $\nabla e_n$. Then I will discuss a recent conjecture involving these two symmetric...

28. The proper conflict-free $k$-coloring problem and the odd $k$-coloring problem are NP-complete on bipartite graphs

Mr Jungho Ahn (KAIST & IBS DIMAG)

01/10/2022, 15:40

Contributed talk

A proper coloring of a graph is proper conflict-free if every non-isolated vertex $v$ has a neighbor whose color is unique in the neighborhood of $v$.
A proper coloring of a graph is odd if for every non-isolated vertex $v$, there is a color appearing an odd number of times in the neighborhood of $v$.
For an integer $k$, the PCF $k$-Coloring problem asks whether an input graph admits a...