THE STRUCTURE OF SYMMETRY GROUPS OF ALMOST PERFECT ONE FACTORIZATIONS

THE STRUCTURE OF SYMMETRY GROUPS OF ALMOST PERFECT ONE FACTORIZATIONS

The concept of j-perfection of a one factorization is introduced. A one factorization is perfect if and only if it is 2-perfect. We call 3-perfect one factorizations almost perfect one-factorizations (or APOFs). First we give some general results concerning the automorphism groups of j-perfect one f...

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Veröffentlicht in:The Rocky Mountain journal of mathematics 2000-06, Vol.30 (2), p.529-554
Hauptverfasser: DUNCAN, DELLA, IHRIG, EDWIN
Format: Artikel
Sprache:eng
Schlagworte:
Automorphisms
Cardinality
Even numbers
Factorization
Group structure
Integers
Vertices
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Zusammenfassung:The concept of j-perfection of a one factorization is introduced. A one factorization is perfect if and only if it is 2-perfect. We call 3-perfect one factorizations almost perfect one-factorizations (or APOFs). First we give some general results concerning the automorphism groups of j-perfect one factorizations, and then we classify all APOFs which have more than one automorphism of order two with fixed points. Several structure theorems for the automorphism groups of APOFs are also given.
ISSN:0035-7596
1945-3795
DOI:10.1216/rmjm/1022009279