6 citations · 14 across the 9 of their papers we have counts for
18 papers
Latin Squares with Few Transversals
Zur Luria
Let denote the minimum number of transversals in a Latin square of odd order . Improving upon a recent bound of Dai, Divoux and Kelly, we prove that for every such th…
More Vertices of the Tristochastic Polytope
Nati Linial, Zur Luria, Maya Trakhtman
The doubly stochastic matrices constitute a polytope in , and by Birkhoff's theorem, its vertex set coincides with the set of order- permutation ma…
A lower bound for the -queens problem
Zur Luria, Michael Simkin
The -queens puzzle is to place mutually non-attacking queens on an chessboard. We present a simple two stage randomized algorithm to construct such configuratio…
On simple connectivity of random 2-complexes
Zur Luria, Yuval Peled
The fundamental group of the -dimensional Linial-Meshulam random simplicial complex was first studied by Babson, Hoffman and Kahle. They proved that the threshold pro…
Perfect Matchings in Random Subgraphs of Regular Bipartite Graphs
Roman Glebov, Zur Luria, Michael Simkin
Consider the random process in which the edges of a graph are added one by one in a random order. A classical result states that if is the complete graph or the co…
On the Threshold Problem for Latin Boxes
Zur Luria, Michael Simkin
Let . An 0-1 array is a Latin box if it contains exactly ones, and has at most one in each line. As a special case, Latin boxes in w…
New bounds on the number of n-queens configurations
Zur Luria
In how many ways can queens be placed on an chessboard so that no two queens attack each other? This is the famous -queens problem. Let denote the number…
A Sharp Threshold for Spanning 2-Spheres in Random 2-Complexes
Zur Luria, Ran J. Tessler
A Hamiltonian cycle in a graph is a spanning subgraph that is homeomorphic to a circle. With this in mind, it is natural to define a Hamiltonian d-sphere in a d-dimensional simplic…
On groups and simplicial complexes
Alexander Lubotzky, Zur Luria, Ron Rosenthal
The theory of -regular graphs is closely related to group theory. Every -regular, bipartite graph is a Schreier graph with respect to some group , a set of generators …
Random Steiner systems and bounded degree coboundary expanders of every dimension
Alexander Lubotzky, Zur Luria, Ron Rosenthal
We introduce a new model of random -dimensional simplicial complexes, for , whose -cells have bounded degrees. We show that with high probability, complexes samp…
The number of Hamiltonian decompositions of regular graphs
Roman Glebov, Zur Luria, Benny Sudakov
A Hamilton cycle in a graph is a cycle passing through every vertex of . A Hamiltonian decomposition of is a partition of its edge set into disjoint Hamilton cycles. One…
Discrepancy of High-Dimensional Permutations
Nathan Linial, Zur Luria
Let be an order- Latin square. For , let be the number of triples such that . We conjectur…
On the maximum number of Latin transversals
Roman Glebov, Zur Luria
Let denote the maximal number of transversals in an order- Latin square. Improving on the bounds obtained by McKay et al., Taranenko recently proved that $T(n) \leq \left…
Chernoff's Inequality - A very elementary proof
Nathan Linial, Zur Luria
We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.
On the vertices of the d-dimensional Birkhoff polytope
Nathan Linial, Zur Luria
Consider the Birkhoff polytope of n by n doubly-stochastic matrices. As the Birkhoff-von Neumann theorem famously states, its vertex set coincides with the set of all n by n permut…
An Upper bound on the number of Steiner triple systems
Nathan Linial, Zur Luria
Let STS(n) denote the number of Steiner triple systems on n vertices, and let F(n) denote the number of 1-factorizations of the complete graph on n vertices. We prove the following…
An upper bound on the number of high-dimensional permutations
Nathan Linial, Zur Luria
What is the higher-dimensional analog of a permutation? If we think of a permutation as given by a permutation matrix, then the following definition suggests itself: A d-dimensiona…
An approximation algorithm for counting contingency tables
Alexander Barvinok, Zur Luria, Alex Samorodnitsky +1
We present a randomized approximation algorithm for counting contingency tables, mxn non-negative integer matrices with given row sums R=(r_1, ..., r_m) and column sums C=(c_1, ...…