Loops, latin squares and strongly regular graphs: An algorithmic approach via algebraic combinatorics

Aiso Heinze; Mikhail Klin

doi:10.1007/978-3-642-01960-9_1

Loops, latin squares and strongly regular graphs: An algorithmic approach via algebraic combinatorics

Aiso Heinze
, Mikhail Klin

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

7 Scopus citations

Abstract

Using in conjunction computer packages GAP and COCO we establish an efficient algorithmic approach for the investigation of automorphism groups of geometric Latin square graphs. With the aid of this approach an infinite series of proper loops is presented which have a sharply transitive group of collineations. The interest in such loops was expressed by A. Barlotti and K. Strambach.

Original language	English
Title of host publication	Algorithmic Algebraic Combinatorics and Gröbner Bases
Publisher	Springer Berlin Heidelberg
Pages	3-65
Number of pages	63
ISBN (Print)	9783642019593
DOIs	https://doi.org/10.1007/978-3-642-01960-9_1
State	Published - 1 Dec 2009

Keywords

Association scheme
Computer algebra
Latin square graph
Loop
Net
Partial difference set
Regular subgroup
Transversal design

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-642-01960-9_1

Cite this

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abstract = "Using in conjunction computer packages GAP and COCO we establish an efficient algorithmic approach for the investigation of automorphism groups of geometric Latin square graphs. With the aid of this approach an infinite series of proper loops is presented which have a sharply transitive group of collineations. The interest in such loops was expressed by A. Barlotti and K. Strambach.",

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N2 - Using in conjunction computer packages GAP and COCO we establish an efficient algorithmic approach for the investigation of automorphism groups of geometric Latin square graphs. With the aid of this approach an infinite series of proper loops is presented which have a sharply transitive group of collineations. The interest in such loops was expressed by A. Barlotti and K. Strambach.

AB - Using in conjunction computer packages GAP and COCO we establish an efficient algorithmic approach for the investigation of automorphism groups of geometric Latin square graphs. With the aid of this approach an infinite series of proper loops is presented which have a sharply transitive group of collineations. The interest in such loops was expressed by A. Barlotti and K. Strambach.

KW - Association scheme

KW - Computer algebra

KW - Latin square graph

KW - Loop

KW - Net

KW - Partial difference set

KW - Regular subgroup

KW - Transversal design

UR - https://www.scopus.com/pages/publications/84885760171

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M3 - Chapter

AN - SCOPUS:84885760171

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SP - 3

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BT - Algorithmic Algebraic Combinatorics and Gröbner Bases

PB - Springer Berlin Heidelberg

ER -

Loops, latin squares and strongly regular graphs: An algorithmic approach via algebraic combinatorics

Abstract

Keywords

ASJC Scopus subject areas

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