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117
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COMBINATORICA
2008
84views more  COMBINATORICA 2008»
15 years 1 months ago
Parity check matrices and product representations of squares
Let NF(n, k, r) denote the maximum number of columns in an n-row matrix with entries in a finite field F in which each column has at most r nonzero entries and every k columns are...
Assaf Naor, Jacques Verstraëte
103
Voted
CORR
2010
Springer
102views Education» more  CORR 2010»
15 years 1 months ago
Structure of random r-SAT below the pure literal threshold
It is well known that there is a sharp density threshold for a random r-SAT formula to be satisfiable, and a similar, smaller, threshold for it to be satisfied by the pure literal ...
Alexander D. Scott, Gregory B. Sorkin
EJC
2007
15 years 1 months ago
Bart-Moe games, JumbleG and discrepancy
Let A and B be hypergraphs with a common vertex set V . In a (p, q, A ∪ B) Bart-Moe game, the players take turns selecting previously unclaimed vertices of V . The game ends whe...
Dan Hefetz, Michael Krivelevich, Tibor Szabó...
122
Voted
TOC
2008
122views more  TOC 2008»
15 years 1 months ago
Derandomizing the Ahlswede-Winter matrix-valued Chernoff bound using pessimistic estimators, and applications
: Ahlswede and Winter [IEEE Trans. Inf. Th. 2002] introduced a Chernoff bound for matrix-valued random variables, which is a non-trivial generalization of the usual Chernoff bound ...
Avi Wigderson, David Xiao
JCT
2010
109views more  JCT 2010»
15 years 9 days ago
Avoider-Enforcer: The rules of the game
An Avoider-Enforcer game is played by two players, called Avoider and Enforcer, on a hypergraph F ⊆ 2X . The players claim previously unoccupied elements of the board X in turns...
Dan Hefetz, Michael Krivelevich, Milos Stojakovic,...