FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2013, VOLUME 18, NUMBER 1, PAGES 21-34

Representations of the strong endomorphism monoid of finite $n$-uniform hypergraphs

E. A. Bondar
Yu. V. Zhuchok

Abstract

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In this paper, two exact representations of the strong endomorphism monoid of an arbitrary finite $n$-uniform hypergraph are described. It is proved that the strong endomorphism monoid of a finite $n$-uniform hypergraph is regular. We find all nonnegative integers $n$ such that $n$-uniform hypergraphs are determined by their strong endomorphisms.

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Last modified: September 5, 2013