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Abstract: We construct a system H of exp(c log 2 n= log log n) subsets of a set of n elements such that the size of each set is divisible by 6 but their pairwise intersections are not divisible by 6. The result generalizes to all non-prime-power moduli m in place of m = 6. This result is in sharp contrast with results of Frankl and Wilson (1981) for prime power moduli and gives strong negative answers to questions by Frankl and Wilson (1981) and Babai and Frankl (1992). We use our set-system H to... (Update)
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...due to Frankl and Wilson [3] gives a graph with exp ( 1 Gamma ) log t) log log t vertices. We proved matching bounds in [5], with a method generalizable to explicit Ramsey colorings with more than two colors. In the paper [4] we have found a relation between low rank...
Cited by: More
The Degree of Threshold mod 6 and Diophantine Equations - Nayantara Bhatnagar College (Correct)
Computing Elementary Symmetric Polynomials with a Sub-Polynomial .. - Grolmusz (2002) (Correct)
A Note on Explicit Ramsey Graphs and Modular Sieves - Grolmusz (Correct)
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0.5: Set Systems With Restricted Intersections Modulo Prime.. - Babai, Frankl, Kutin.. (2001) (Correct)
0.1: Erdös on Unit Distances and the Szemerédi-Trotter Theorems - Székely (Correct)
0.1: On Set Systems with Restricted Intersections Modulo a Composite.. - Grolmusz (1996) (Correct)
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0.9: Set-Systems with Restricted Multiple Intersections - Grolmusz (2002) (Correct)
0.8: A Lower Bound On The Mod 6 Degree Of The Or Function - Tardos, Barrington (1995) (Correct)
0.3: Constructing Set-Systems with Prescribed Intersection Sizes - Grolmusz (2001) (Correct)
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8: Linear Algebra Methods in Combinatorics (context) - Babai, Frankl - 1988
8: Intersection Theorem with Geometric Consequences (context) - Frankl, Wilson - 1981
6: A lower bound on the MOD 6 degree of the OR function - bor, David et al. - 1995
BibTeX entry: (Update)
V. Grolmusz, Superpolynomial size set systems with restricted intersections mod 6 and explicit Ramsey graphs, Combinatorica, to appear. (Preliminary version in: Lecture Notes in Computer Science Vol. 1276, 1997, 82-90.) http://citeseer.ist.psu.edu/grolmusz99superpolynomial.html More
@article{ grolmusz00superpolynomial,
author = "Vince Grolmusz",
title = "Superpolynomial Size Set-systems with Restricted Intersections mod 6 and Explicit Ramsey Graphs",
journal = "Combinatorica",
volume = "20",
number = "1",
pages = "71-86",
year = "2000",
url = "citeseer.ist.psu.edu/grolmusz99superpolynomial.html" }
Citations (may not include all citations):43 Linear algebra methods in combinatorics (context) - Babai, Frankl - 1992
35 Intersection theorems with geometric consequences (context) - Frankl, Wilson - 1981
10 Some remarks on the theory of graphs (context) - os - 1947
10 A counterexample to Borsuk's conjecture (context) - Kahn, Kalai - 1993
2 Constructing nite sets with given intersections (context) - Frankl - 1983
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.math.elte.hu/~grolmusz/):
Low Rank Co-Diagonal Matrices and Ramsey Graphs - Grolmusz (2000) (Correct)
A Note on Set Systems with no Union of Cardinality 0 Modulo m - Grolmusz (2000) (Correct)
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