KPPY 92

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

KPPY 92

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
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
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 known as absolute if a graph strongly regular. in 2003, bell rowlinson extended this to any eigenvalue $a$ distinct from $0$ or $-1$, showed that graphs attaining equality are extremal regular (the only examples pentagon, complete multipartite graph, schl\"{a}fli mclaughlin their complements). talk i will discuss bounds for eigenvalues hermitian adjacency matrices digraphs.

This talk is based on joint work with Sho Suda.
Seung Yeop Yang
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 $p^2$
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.
Alex Wires
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.