Sum complexes - a new family of hypertrees (2009)
Linial, Nathan, Meshulam, Roy, Rosenthal, Mishael
A k-dimensional hypertree X is a k-dimensional complex on n vertices with a full (k-1)-dimensional skeleton and \binom{n-1}{k} facets such that H_k(X;Q)=0. Here we introduce the following family of...
Alexander Lubotzky, Roy Meshulam
Let X be a d-dimensional simplicial complex with N faces of dimension d − 1. Suppose that every (d − 1)-face of X is contained in at least k � d + 2 faces of X, of dimension d. Extending the...
Leray numbers of projections and a topological Helly-type theorem (2008)
Let X be a simplicial complex on the vertex set V. The rational Leray number of X is the minimal d, such that for all induced subcomplexes Y ⊂ X and i ⩾ d. Suppose that is a partition of...
On the Number of Flats Spanned by a Set of Points in ... (2007)
It is shown that for fixed 1 # r # s < d and # > 0, if X # PG(d, q) contains (1+#)q s points, then the number of r-flats spanned by X is at least c(#)q (r+1)(s+1-r) , i.e. a positive fraction...
A Geometrical Problem Arising in a Signal Restoration Algorithm (2007)
Nir Cohen And, Nir Cohen, Roy Meshulam
Let Z 2N = f0; : : : ; 2N \Gamma 1g denote the group of integers modulo 2N , and let L be the space of all real functions on Z 2N which are supported on f0; : : : ; N \Gamma 1g. The spectral phase of...
Inverse Conjecture for the Gowers norm is false (2007)
Lovett, Shachar, Meshulam, Roy, Samorodnitsky, Alex
Let $p$ be a fixed prime number, and $N$ be a large integer. The 'Inverse Conjecture for the Gowers norm' states that if the "$d$-th Gowers norm" of a function $f:\F_p^N \to \F_p$ is non-negligible,...
Homological Connectivity of Random 2-Complexes (2007)
Let # n-1 denote the (n- 1)-dimensional simplex. Let Y be a random 2-dimensional subcomplex of # n-1 obtained by starting with the full 1-dimensional skeleton of # n-1 and then adding each 2-simplex...
Transversal numbers for hypergraphs arising in geometry (2007)
Noga Alon, Gil Kalai, Roy Meshulam
Ji r ' i Matou sek y
for all (x 1; : : : ; xn) 2 S. The width of a function f j is dened as (2007)
Ron Aharoni, Ron Holzman, Michael Krivelevich, Roy Meshulam
Abstract. In 1950 Bang proposed a conjecture which became known as \the plank conjecture": Suppose that a convex set S contained in the unit cube of
A Moore bound for simplicial complexes (2007)
Lubotzky, Alexander, Meshulam, Roy
Let X be a d-dimensional simplicial complex with N faces of dimension d − 1. Suppose that every (d − 1)-face of X is contained in at least k ≥ d + 2 faces of X, of dimension d. Extending the...
Leray numbers of projections and a topological Helly type theorem (2007)
Let X be a simplicial complex on the vertex set V. The rational Leray number L(X) of X is the minimal d such that the rational reduced homology of any induced subcomplex of X vanishes in dimensions d...
Inverse Conjecture for the Gowers norm is false (2007)
Shachar Lovett, Roy Meshulam, Alex Samorodnitsky
Let p be a fixed prime number, and N be a large integer. The ’Inverse Conjecture for the Gowers norm ’ states that if the ”d-th Gowers norm ” of a function f: F N p → F is non-negligible,...
Leray numbers of projections and a topological Helly type theorem (2007)
Let X be a simplicial complex on the vertex set V. The rational Leray number L(X) of X is the minimal d such that ˜ Hi(Y; Q) = 0 for all induced subcomplexes Y ⊂ X and i ≥ d. Suppose V = �m...
Inverse Conjecture for the Gowers norm is false (2007)
Shachar Lovett, Roy Meshulam, Alex Samorodnitsky
Let p be a fixed prime number, and N be a large integer. The ’Inverse Conjecture for the Gowers norm ’ states that if the ”d-th Gowers norm ” of a function f: F N p → F is non-negligible,...
Kalai (Hebrew University, Jerusalem), and Günter M. Ziegler (TU Berlin). It (2007)
Anders Björner (stockholm, Gil Kalai (jerusalem, Igor Pak, Er Barvinok, Roy Meshulam
Abstract. The 2007 Oberwolfach meeting “Geometric and Topological Combinatorics ” presented a great variety of investigations where topological and algebraic methods are brought into play to...
A Moore bound for simplicial complexes (2007)
Lubotzky, Alexander, Meshulam, Roy
Let X be a d-dimensional simplicial complex with N faces of dimension d − 1. Suppose that every (d − 1)-face of X is contained in at least k ≥ d + 2 faces of X, of dimension d. Extending the...
A Moore bound for simplicial complexes (2007)
Lubotzky, Alexander, Meshulam, Roy
Let X be a d-dimensional simplicial complex with N faces of dimension d − 1. Suppose that every (d − 1)-face of X is contained in at least k ≥ d + 2 faces of X, of dimension d. Extending the...
Intersections of Leray complexes and regularity of monomial ideals (2006)
For a simplicial complex X and a field K, let h_i(X)=\dim \tilde{H}_i(X;K). It is shown that if X,Y are complexes on the same vertex set, then for all k h_{k-1}(X\cap Y) \leq \sum_{\sigma \in Y}...
Intersections of Leray Complexes and Regularity of Monomial Ideals (2005)
For a simplicial complex X and a field K, let ˜ hi(X) = dim ˜ Hi(X; K). It is shown that if X, Y are complexes on the same vertex set, then for k ≥ 0 ˜hk−1(X ∩ Y) ≤ � � ˜hi−1(X[σ])...
An uncertainty inequality for finite abelian groups (2003)
Let G be a finite abelian group of order n. For a complex valued function f on G, let \fht denote the Fourier transform of f. The uncertainty inequality asserts that if f \neq 0 then |supp(f)|...
On representation theory in computer vision problems (2002)
Amnon Shashua, Roy Meshulam, Lior Wolf, Anat Levin, Gil Kalai
We introduce the following general question: Let V be a complex n-dimensional space and for m k consider the GL(V)-module V (n # m # k) ae V
On Representation Theory in Computer Vision (2002)
Problems Amnon Shashua, Amnon Shashua, Roy Meshulam, Lior Wolf, Anat Levin, Gil Kalai
We introduce the following general question: Let V be a complex n-dimensional space and for m k consider the GL(V )-module V (n# m# k)=f v 1 \Omega \Delta\Delta\Delta \Omega vm 2 V We would like to...
Transversal Numbers for Hypergraphs Arising in Geometry (2001)
Noga Alon, Gil Kalai, Roy Meshulam
Introduction Helly's theorem asserts that if F is a nite family of convex sets in R in which every d + 1 or fewer sets have a point in common then F 6= ;. Our starting point, the (p; q) theorem,...
North-Holland COMMUNICATION AN UNCERTAINTY INEQUALITY AND ZERO SUBSUMS (1990)
Roy Meshulam, Communicated J. Kahn
Let G be a finite abelian group, and let m be the maximal order of elements in G. It is shown that if s>m ( l+loglcl then any sequence a,, m 1 ’., a, of elements in G, has a non-empty...