Bruck–Ryser–Chowla theorem
id:
bruck-ryser-chowla-theorem-263-4252745
title:
Bruck–Ryser–Chowla theorem
text:
The Bruck–Ryser–Chowla theorem is a result on the combinatorics of block designs that implies nonexistence of certain kinds of design. It states that if a (v, b, r, k, λ)-design exists with v = b (a symmetric block design), then: if v is even, then k − λ is a square;
if v is odd, then the following Diophantine equation has a nontrivial solution:
x2 − (k − λ)y2 − (−1)(v−1)/2 λ z2 = 0. The theorem was proved in the case of projective planes by Bruck & Ryser (1949). It was extended to symmetric des
brand slug:
wiki
category slug:
encyclopedia
description:
Nonexistence result for combinatorial block designs
original url:
https://en.wikipedia.org/wiki/Bruck%E2%80%93Ryser%E2%80%93Chowla_theorem
date created:
date modified:
2023-11-17T08:20:17Z
main entity:
{"identifier":"Q2226624","url":"https://www.wikidata.org/entity/Q2226624"}
image:
fields total:
13
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