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The existence of Schröder designs with equal-sized holes

✍ Scribed by F.E. Bennett; Ruizhong Wei

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 605 KB
Volume: 170
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00353-x

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✦ Synopsis

A holey Schr6der design of type h"~'h"22 ... h~ k (HSD(h]'h~ .... h~k)) is equivalent to a frame idempotent SchrBder quasigroup (FISQ(h]lh~ .... h~?)) of order n with n~ missing subquasigroups (holes) of order hi, (1 ~< i ~< k), which are disjoint and spanning, that is, ~1 <~ i <~ k nlhi = n. In this paper, it is shown that an HSD(h") exists if and only if hZn(n-1)-0(rood4) with expceptions (h, n) E { (1, 5), (1, 9), (2, 4) } and the possible exception of (h, n) = (6, 4).

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