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# Kevin Hendrey, Covering radius in the Hamming permutation space

## March 24 Tuesday @ 4:30 PM - 5:30 PM KST

Room B232, IBS (기초과학연구원)

### Speaker

Our problem can be described in terms of a two player game, played with the set $\mathcal{S}_n$ of permutations on $\{1,2,\dots,n\}$. First, Player 1 selects a subset $S$ of $\mathcal{S}_n$ and shows it to Player 2. Next, Player 2 selects a permutation $p$ from $\mathcal{S}_n$ as different as possible from the permutations in $S$, and shows it to Player 1. Finally, Player 1 selects a permutation $q$ from $S$, and they compare $p$ and $q$. The aim of Player 1 is to ensure that $p$ and $q$ differ in few positions, while keeping the size of $S$ small. The function $f(n,s)$ can be defined as the minimum size of a set $S\subseteq \mathcal{S}_n$ that Player 1 can select in order to gaurantee that $p$ and $q$ will differ in at most $s$ positions.

I will present some recent results on the function $f(n,s)$. We are particularly interested in determining the value $f(n,2)$, which would resolve a conjecture of Kézdy and Snevily that implies several famous conjectures for Latin squares. Here we improve the best known lower bound, showing that $f(n,2)\geqslant 3n/4$. This talk is based on joint work with Ian M. Wanless.

## Details

Date:
March 24 Tuesday
Time:
4:30 PM - 5:30 PM KST
Event Category:
Event Tags:

Room B232
IBS (기초과학연구원)

## Organizer

Sang-il Oum (엄상일)
Website:
https://dimag.ibs.re.kr/home/sangil/
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209