Near coverings and cosystolic expansion

Autor: Irit Dinur, Roy Meshulam

Publikováno v: Archiv der Mathematik. 118:549-561

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::4733d0add032ff394a7f03c9f0721e69
https://doi.org/10.1007/s00013-022-01720-6

On the topology of complexes of injective words

Autor: Ran Levi, Wojtek Chacholski, Roy Meshulam

Publikováno v: Journal of Applied and Computational Topology. 4:29-44

An injective word over a finite alphabet $V$ is a sequence $w=v_1v_2\cdots v_t$ of distinct elements of $V$. The set $\mathrm{inj}(V)$ of injective words on $V$ is partially ordered by inclusion. A complex of injective words is the order complex $\De

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::05e963d269e5a8f0a07ccaf4661cc4eb
https://doi.org/10.1007/s41468-019-00039-6

Pach’s Selection Theorem Does Not Admit a Topological Extension

Autor: Roy Meshulam, Martin Tancer, Imre Bárány, Eran Nevo

Publikováno v: Discrete & Computational Geometry. 60:420-429

Let $$U_1,\ldots ,U_{d+1}$$ be n-element sets in $$\mathbb {R}^d$$ . Pach’s selection theorem says that there exist subsets $$Z_1\subset U_1,\ldots ,Z_{d+1}\subset U_{d+1}$$ and a point $$u \in \mathbb {R}^d$$ such that each $$|Z_i|\ge c_1(d)n$$ an

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ed3c40c1a55c1032b8e50d879ed1d9e2
https://doi.org/10.1007/s00454-018-9998-8

Spectral expansion of random sum complexes

Autor: Orr Beit-Aharon, Roy Meshulam

Let $G$ be a finite abelian group of order $n$ and let $\Delta_{n-1}$ denote the $(n-1)$-simplex on the vertex set $G$. The sum complex $X_{A,k}$ associated to a subset $A \subset G$ and $k < n$, is the $k$-dimensional simplicial complex obtained by

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::05a5b0e665aa34e2b696342291b342bb
http://arxiv.org/abs/1801.06466

Homology of Spaces of Directed Paths in Euclidean Pattern Spaces

Autor: Roy Meshulam, Martin Raussen

Publikováno v: A Journey Through Discrete Mathematics ISBN: 9783319444789
Meshulam, R & Raussen, M H 2017, Homology of Spaces of Directed Paths in Euclidean Pattern Spaces . in M Loebl, J Nesetril & R Thomas (eds), A Journey Through Discrete Mathematics : A Tribute to Jirí Matousek . Springer, pp. 593-614 . https://doi.org/10.1007/978-3-319-44479-6_24

Let \(\mathcal{F}\) be a family of subsets of {1, …, n} and let $$\displaystyle{ Y _{\mathcal{F}} =\bigcup _{F\in \mathcal{F}}\{(x_{1},\ldots,x_{n}) \in \mathbb{R}^{n}: x_{ i} \in \mathbb{Z}\text{for all}i \in F\}. }$$ Let \(X_{\mathcal{F}} = \math

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::85698cd0743562b3ad717c11f81e36f6
https://doi.org/10.1007/978-3-319-44479-6_24