On a combinatorial problem from the model theory of wreath products. II
type: Item
instance of: scholarly article
title: On a combinatorial problem from the model theory of wreath products. II
zbMATH Open document ID: 0928.03042
author: Dan Saracino
published in: Journal of Combinatorial Theory. Series A
publication date: 1999-07-20T00:00:00Z
review text: Given integers \(r\), \(n\) with \(2\leq n\leq r\), denote by \(\delta(n,r)\) the least integer \(d\) for which there are disjoint multisets \(\{E_1,\dots, E_d\}\) and \(\{E_1',\dots, E_d'\}\) of equivalence relations on a set \(X\) of \(r\) elements such that each relation has at most \(n\) classes, at least one of them actually has \(n\) nonempty classes, and for each \(x\in X\) the restrictions of the \(E_j\) to \(X\setminus\{x\}\) coincide in some order with the restrictions of the \(E_j'\) to \(X\setminus\{x\}\). The numbers \(\delta(n,r)\) arise in the model-theoretic investigations of wreath products. The author gives the explicit values of \(\delta(n,r)\) for all arguments \(n\), \(r\). In Part I he proves the values for \(n=3\), in Part II those for \(n=4\).
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 05A18
Mathematics Subject Classification ID: 20E22
zbMATH DE Number: 1295470
zbMATH Keywords: equivalence relations
zbMATH Keywords: model-theoretic investigations of wreath products
reviewed by: Jörg Flum
MaRDI profile type: Publication
full work available at URL: jcta.1998.2940
OpenAlex ID: W4213033431
cites work: Q4764102
cites work: Arities of permutation groups: Wreath products and \(k\)-sets
DOI: 10.1006/JCTA.1998.2940
description: scientific article; zbMATH DE number 1295470