Generalization of k-uniform hypergraphons

Alsowait, Nawaf (2022) Generalization of k-uniform hypergraphons. Doctoral thesis, University of East Anglia.

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Abstract

This thesis studies a generalization of the k-uniform hypergraphons by working with an arbitrary space. In particular, we offer two different generalizations: k-uniform hypergraphons and k-uniform mixed hypergraphons. Motivated by results on graphons, we reduce every k-uniform hypergraphon to a twin-free separable k-uniform hypergraphon. Moreover, we prove that every k-uniform hypergraphon is weakly isomorphic to a twin-free separable k-uniform hypergraphon. However, we find a counterexample which shows the notion of k-uniform hypergraphon does not satisfy the purity conditions. Therefore, we construct a new generalization, the k-uniform mixed hypergraphon, that helps us to prove every twin-free separable k-uniform mixed hypergraphon is weakly ismomorphic to a pure k-uniform mixed hypergraphon. Furthermore, we show that every twin-free separable k-uniform mixed hypergraphon is isomorphic, up to a null set, to a pure k-uniform mixed hypergraphon.

Item Type:	Thesis (Doctoral)
Faculty \ School:	Faculty of Science > School of Mathematics
Depositing User:	Chris White
Date Deposited:	19 Aug 2022 09:50
Last Modified:	19 Aug 2022 09:50
URI:	https://ueaeprints.uea.ac.uk/id/eprint/87497
DOI:

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