Recent Comments

Recent Posts
 Mathematical Gymnastics
 Media Item from “Haaretz” Today: “For the first time ever…”
 Jim Geelen, Bert Gerards, and Geoﬀ Whittle Solved Rota’s Conjecture on Matroids
 Media items on David, Amnon, and Nathan
 Next Week in Jerusalem: Special Day on Quantum PCP, Quantum Codes, Simplicial Complexes and Locally Testable Codes
 Happy Birthday Ervin, János, Péter, and Zoli!
 My Mathematical Dialogue with Jürgen Eckhoff
 Test Your Intuition (23): How Many Women?
 Happy Birthday Richard Stanley!
Top Posts & Pages
 The KadisonSinger Conjecture has beed Proved by Adam Marcus, Dan Spielman, and Nikhil Srivastava
 Mathematical Gymnastics
 Believing that the Earth is Round When it Matters
 Media Item from "Haaretz" Today: "For the first time ever..."
 The Ultimate Riddle
 Two Math Riddles
 New Ramanujan Graphs!
 Amazing: Peter Keevash Constructed General Steiner Systems and Designs
 Why Quantum Computers Cannot Work: The Movie!
RSS
Tag Archives: Extremal combinatorics
Analysis of Boolean Functions – week 1
Home page of the course. In the first lecture I defined the discrete ndimensional cube and Boolean functions. Then I moved to discuss five problems in extremal combinatorics dealing with intersecting families of sets. 1) The largest possible intersecting family … Continue reading
Cup Sets, Sunflowers, and Matrix Multiplication
This post follows a recent paper On sunflowers and matrix multiplication by Noga Alon, Amir Spilka, and Christopher Umens (ASU11) which rely on an earlier paper Grouptheoretic algorithms for matrix multiplication, by Henry Cohn, Robert Kleinberg, Balasz Szegedy, and Christopher Umans (CKSU05), … Continue reading
Extremal Combinatorics on Permutations
We talked about extremal problems for set systems: collections of subsets of an element sets, – Sperner’s theorem, the ErdosKoRado theorem, and quite a few more. (See here, here and here.) What happens when we consider collections of permutations rather … Continue reading
Posted in Combinatorics
Tagged ErdosKoRado theorem, Extremal combinatorics, Permutations
9 Comments
FranklRodl’s Theorem and Variations on the Cap Set Problem: A Recent Research Project with Roy Meshulam (A)
Voita Rodl I would like to tell you about a research project in progress with Roy Meshulam. (We started it in the summer, but then moved to other things; so far there are interesting insights, and perhaps problems, but not substantial … Continue reading
Posted in Combinatorics, Open problems
Tagged Cap sets, Extremal combinatorics, Intersection theorems, polymath1
6 Comments
Lovasz’s Two Families Theorem
Laci and Kati This is the first of a few posts which are spinoffs of the extremal combinatorics series, especially of part III. Here we talk about Lovasz’s geometric two families theorem. 1. Lovasz’s two families theorem Here … Continue reading
Posted in Combinatorics, Convexity, Open problems
Tagged exterior algebras, Extremal combinatorics, shellability
5 Comments
Extremal Combinatorics IV: Shifting
Compression We describe now a nice proof technique called “shifting” or “compression” and mention a few more problems. The SauerShelah Lemma: Let . Recall that a family shatters a set if for every there is such that … Continue reading
Extremal Combinatorics III: Some Basic Theorems
. Shattering Let us return to extremal problems for families of sets and describe several basic theorems and basic open problems. In the next part we will discuss a nice proof technique called “shifting” or “compression.” The SauerShelah (Perles VapnikChervonenkis) Lemma: (Here we write .) … Continue reading
Extermal Combinatorics II: Some Geometry and Number Theory
Extremal problems in additive number theory Our first lecture dealt with extremal problems for families of sets. In this lecture we will consider extremal problems for sets of real numbers, and for geometric configurations in planar Euclidean geometry. Problem I: Given a set A of … Continue reading
Local Events, Turan’s Problem and Limits of Graphs and Hypergraphs
I will write a little about how hectic things are now here at HU, and make two (somewhat related) followups on previous posts: Tell you about Turan’s problem, and about Balázs Szegedi’s lecture from Marburg dealing with limits of graphs and hypergraphs. Local Events … Continue reading
Posted in Combinatorics, Open problems
Tagged Extremal combinatorics, Graph limits, Quasirandomness, Turan's problem
3 Comments
Extremal Combinatorics I: Extremal Problems on Set Systems
The “basic notion seminar” is an initiative of David Kazhdan who joined HU math department around 2000. People give series of lectures about basic mathematics (or not so basic at times). Usually, speakers do not talk about their own research and not even … Continue reading