A következő kombinatorika szemináriumok ideje

július 25. (!!! PÉNTEK !!!), !!! 11:00- !!!,

helye

!!! Bolyai Intézet, Aradi Vértanúk tere, Szőkefalvi-Nagy terem !!! (második emelet, a folyosó kanyarában)
és előadásai:

11:00 Hong Liu (UIUC): The number of maximal sum-free subsets of integers

Joint work with Jozsef Balogh, Maryam Sharifzadeh and Andrew Treglown

Abstract: Cameron and Erdős raised the question of how many maximal sum-free sets there are in {1,...,n}, giving a lower bound of 2\lfloor n/4 \rfloor. In this paper we prove that there are in fact at most $2(1/4+o(1))n maximal sum-free sets in {1,..., n}.

Our proof makes use of `container' and `removal' lemmas of Green as well as a result of Deshouillers, Freiman, Sós and Temkin on the structure of sum-free sets.

11:45 Michelle Delcourt (UIUC): The Typical Structure of Intersecting Families

Enumerating families of combinatorial objects with given properties and describing the typical structure of these objects are fundamental problems in extremal combinatorics. During this talk, we will focus in particular on the structure of t-intersecting families of permutations on [n]. If time permits, we will explore the structure of intersecting families in a variety of other settings. Main tools include generalizations of the Bollobás set-pairs inequality and Ellis's stability theorem for intersecting families of permutations. This is joint work with József Balogh, Shagnik Das, Hong Liu, and Maryam Sharifzadeh.

Mindenkit szeretettel várunk,

Peter

Supported by TÁMOP-4.2.2.A-11/1/KONV-2012-0073, Telemedicine Oriented Research in the Fields of Mathematics, Informatics and Medical Sciences