# KPPY 75

Kijung Kim, Jongyoon Hyun, Jihye Park, Seok Joong Kim, Jang Soo Kim

March 26, 2016. 11am - 5:30pm at Postech

Schedule | ||

11:00am - 11:50 |
Kijung Kim PNU | A construction of non-Schurian Schur rings |

12pm - 1:25 | Lunch | |

1:30 - 2:20 |
Jongyoon Hyun KIAS | Introduction to metrices on finite directed graphs |

2:30 - 3:20 |
Jihye Park Yeungnam university | Skew-morphisms of regular Cayley maps |

3:30 - 4:20 |
Seok Joong Kim KNU | Euler's conjecture for latin squares |

4:30 - 5:20 |
Jang Soo Kim Sungkyunkwan university | The q-Selberg integral and reverse plane partitions |

## Abstracts

Kijung Kim

A construction of non-Schurian Schur rings

A construction of non-Schurian Schur rings

Let $H$ be a finite group.
We denote by $\mathbb{Q}H$ the group algebra of $H$ over the rational number field $\mathbb{Q}$.
For a nonempty subset $T \subseteq H$, we set $\underline{T}:= \sum_{t \in T}t$ which is treated as an element of $\mathbb{Q}H$.
A subalgebra $\mathcal{A}$ of the group algebra $\mathbb{Q}H$ is called a

*Schur ring*(briefly*S-ring*) over $H$ if there exists a partition $\mathrm{Bsets}(\mathcal{A}):= \{ T_0, T_1, \dotsc, T_r \}$ of $H$ satisfying the following conditions:- $\{ \underline{T_i} \mid T_i \in \mathrm{Bsets}(\mathcal{A}) \}$ is a linear basis of $\mathcal{A}$;
- $T_0 = \{ 1_H\}$;
- $T_i^{-1}:=\{ t^{-1} \mid t \in T_i \} \in \mathrm{Bsets}(\mathcal{A})$ for all $T_i \in \mathrm{Bsets}(\mathcal{A})$.

Jongyoon Hyun

Introduction to metrices on finite directed graphs

Introduction to metrices on finite directed graphs

In this talk, I introduce metrices on finite directed graphs, very recently developed by Etzion and Firer.
This concept is a generalization of poset metrics introduced by Brualdi, et.al. The related problem is also presented.

Jihye Park

Skew-morphisms of regular Cayley maps

Skew-morphisms of regular Cayley maps

A Cayley map is a 2-cell embedding of a Cayley graph
in orientable surface with the same orientation at each vertex.
The concept of a skew-morphism generalizes several concepts previously
studied with respect to regular Cayley maps, and allows for unified theory
of regular Cayley maps and their automorphism groups. [R. Jajcay, J. Siran,
Skew-morphisms of regular Cayley maps, Discrete Mathematics 244 (2002), 167-179]
In this talk, we give an overview of the Skew-morphisms of regular Cayley maps,
and present recent results.

Seok Joong Kim

Euler's conjecture for latin squares

Euler's conjecture for latin squares

In this presentation, I introduce Euler's conjecture for latin squares.
Furthermore, I want to introduce some examples of latin squares
and an open problem of latin hypercubes.

Jang Soo Kim

The q-Selberg integral and reverse plane partitions

The q-Selberg integral and reverse plane partitions

In this talk we will introduce a combinatorial interpretation for q-integrals.
Then we will show that Askey's q-Selberg integral can be restated as the generating function
for the reverse plane partitions contained in a square with certain weights.
As a special case we obtain the well known "trace" generating function for the reverse plane partitions.