# KPPY 92

Norihide Tokushige, Alexander Gavrilyuk, Seung Yeop Yang, Abbas Wasim, Alex Wires

May 25, 2019. 11am - 5:30pm at KNU

Schedule | ||

11:00am - 11:50 |
Norihide Tokushige University of the Ryukyus, Japan | Muirhead's inequality and a maximal flow |

12pm - 1:25 | Lunch | |

1:30 - 2:20 |
Alexander Gavrilyuk PNU | On the multiplicities of digraph eigenvalues |

2:30 - 3:20 |
Seung Yeop Yang KNU | On the realization of plucking polynomials of rooted plane trees |

3:30 - 4:20 |
Abbas Wasim PNU | On $p$-valenced association schemes whose thin residue has valency $p^2$ |

4:30 - 5:20 |
Alex Wires Southwestern University of Finance and Economics, China | Surjective Polymorphisms of Finite Reflexive Tournaments |

## Abstracts

Norihide Tokushige

Muirhead's inequality and a maximal flow

Muirhead's inequality and a maximal flow

I will present a conjecture concerning an inequality coming from a problem
in extremal set theory. Then I will explain how to prove the inequality for
small parameters. For the proof we use the Muirhead's inequality on
monomial symmetric functions combined with searching a maximal flow in
the corresponding bipartite graph.

Alexander Gavrilyuk

On the multiplicities of digraph eigenvalues

On the multiplicities of digraph eigenvalues

In 1977, Delsarte, Goethals, and Seidel showed that a regular (simple)
graph on $n$ vertices,
whose $(0,1)$-adjacency matrix $A$ has the smallest eigenvalue $<-1$
of multiplicity $n-d$,
satisfies $n\leq \frac{1}{2}d(d+1)-1$. The bound is sharp, and it is
known as the absolute bound
if a graph is strongly regular. In 2003, Bell and Rowlinson extended
this bound to any eigenvalue
of $A$ distinct from $0$ or $-1$, and showed that the graphs attaining
equality are extremal
strongly regular graphs (the only examples known are a pentagon, a
complete multipartite graph,
the Schl\"{a}fli graph, the McLaughlin graph and their complements).
In this talk I will discuss
the multiplicity bounds for eigenvalues of Hermitian adjacency
matrices of digraphs.

This talk is based on joint work with Sho Suda.

This talk is based on joint work with Sho Suda.

Seung Yeop Yang

On the realization of plucking polynomials of rooted plane trees

On the realization of plucking polynomials of rooted plane trees

In 2016, Przytycki introduced a $q$-polynomial invariant of rooted plane trees which can be defined by the product of Gaussian binomial coefficients. It is called the plucking polynomial of a rooted plane tree.
In this talk, we discuss necessary and sufficient conditions for a given polynomial to be the plucking polynomial of a rooted plane tree.

Abbas Wasim

On $p$-valenced association schemes whose thin residue has valency $p^2$

On $p$-valenced association schemes whose thin residue has valency $p^2$

In this talk, we focus on $\{1,3\}$-schemes. In my talk I am going to prove that
$\{1,3\}$-schemes whose thin residues are isomorphic to $C3|C3$ and for which each relation out of thin residue has valency $3$, are finite.

This is joint work with Mitsugu Hirasaka.

This is joint work with Mitsugu Hirasaka.

Alex Wires

Surjective Polymorphisms of Finite Reflexive Tournaments

Surjective Polymorphisms of Finite Reflexive Tournaments

While the idempotent polymorphisms of finite reflexive tournaments can be fairly well-understood, we consider to what extent this is true for the surjective polymorphisms. Recent motivations coming from the Surjective H-Colouring and Quantified Constraint Satisfaction Problems.

Joint work with Barnaby Martin and Petar Markovic.

Joint work with Barnaby Martin and Petar Markovic.