Publication

An improvement on the number of simplices in F-q(d)

Van Thang Pham
2017
Journal Articles

Abstract

Let epsilon be a set of points in F-q(d). Bennett et al. (2016) proved that if \epsilon\ >> [GRAHICS] then epsilon determines a positive proportion of all k-simplices. In this paper, we give an improvement of this result in the case when epsilon is the Cartesian product of sets. Namely, we show that if kd epsilon is the Cartesian product of sets and [GRAHICS] = o(\epsilon), the number of congruence classes of k-simplices determined by epsilon is at least (1 - omicron(1)) [GRAPHICS] , and in some cases our result is sharp. (C) 2017 Elsevier B.V. All rights reserved.

Official source

https://infoscience.epfl.ch/entities/publication/0118f0eb-98dc-474f-a30f-9764cab1798e

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Van Thang Pham
2017
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/0118f0eb-98dc-474f-a30f-9764cab1798e

About this result

Related concepts (32)

Set (mathematics)

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics.

Simplicial set

In mathematics, a simplicial set is an object composed of simplices in a specific way. Simplicial sets are higher-dimensional generalizations of directed graphs, partially ordered sets and . Formally, a simplicial set may be defined as a contravariant functor from the to the . Simplicial sets were introduced in 1950 by Samuel Eilenberg and Joseph A. Zilber. Every simplicial set gives rise to a "nice" topological space, known as its geometric realization.

Fuzzy set

In mathematics, fuzzy sets (a.k.a. uncertain sets) are sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotfi A. Zadeh in 1965 as an extension of the classical notion of set. At the same time, defined a more general kind of structure called an L-relation, which he studied in an abstract algebraic context. Fuzzy relations, which are now used throughout fuzzy mathematics and have applications in areas such as linguistics , decision-making , and clustering , are special cases of L-relations when L is the unit interval [0, 1].

Related publications (32)

An improvement on the number of simplices in F-q(d)

Chat with Graph Search

Hitting with Probability One for Stochastic Heat Equations with Additive Noise

Dynamical system approach to navigation around obstacles

A Note on Lenses in Arrangements of Pairwise Intersecting Circles in the Plane