GT et PÉC de l'équipe Combinatoire et Interactions
The Combinatoire et Interactions seminar runs every Monday from 10h45 to 11h45. There is also a reserved schedule for a "mini-school" from 9h30 to 10h30. Both events happen in room 076 on the ground floor of LaBRI (building A30).
When a talk is recored it is available (live and recorded) at
https://u-bordeaux-fr.zoom.us/j/83326403471?pwd=VLapX1qCOgASs3V8OktWtKEr8dn041.1
Meeting ID: 833 2640 3471
Passcode: 1251442
Contact the secretary (Vincent Delecroix) if you want to propose a talk or to receive announcements.
For the list of previous talks, look at the menu "GT CI" on the right side of this page.
2024-2025
Lundi 21 avril: lundi de Pâques
Lundi 28 avril: vacances de printemps
Lundi 5 mai: à saisir
pique-nique d'équipe en 76
Lundi 12 mai: Gilles Zemor
Titre: Kneser's Theorem for codes and l-divisible set families.
Abstract:
A k-wise l-divisible set family is a collection F of subsets of {1, ...,n} such that any intersection of k sets in F has cardinality divisible by l. If k=l=2, it is well-known that |F| <= 2^{\lfloor n/2 \rfloor}. We generalise this by proving that |F| <= 2^{\lfloor n/p\rfloor}$ if k=l=p, for any prime number p.
For arbitrary values of l, we prove that (4l^2)-wise l-divisible set families F satisfy |F| <= 2^{\lfloor n/l \rfloor} and that the only families achieving the upper bound are atomic, meaning that they consist of the unions of disjoints subsets of size l. This improves upon a recent result by Gishboliner, Sudakov and Timon, that arrived at the same conclusion for k-wise l-divisible families, with values of k that behave exponentially in l.
Our techniques rely heavily upon a coding-theory analogue of Kneser's Theorem from additive combinatorics.
Joint work with Chenying Lin
Lundi 19 mai: Sean Raymond (laboratoire d'astrophysique de Bordeaux)
Lundi 26 mai: Alessandro Giachetto
Lundi 2 juin: Jarkko Kari
pique-nique d'équipe en 76
Lundi 9 juin: pentecôte
Lundi 16 juin: à saisir
Lundi 23 juin: Raquel Melgar
Lundi 30 juin: à saisir