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Journal article
Completing partial transversals of Cayley tables of Abelian groups
The Electronic Journal of Combinatorics, Vol.28(3), P3.60
28
2021
Web of Science ID: WOS:000701859000004
Abstract
In 2003 Grüttmüller proved that if n ⩾ 3 is odd, then a partial transversal of the Cayley table of ℤₙ with length 2 is completable to a transversal. Additionally, he conjectured that a partial transversal of the Cayley table of ℤₙ with length k is completable to a transversal if and only if n is odd and either n ∈ {k, k + 1} or n ⩾ 3k - 1. Cavenagh, Hämäläinen, and Nelson (in 2009) showed the conjecture is true when k = 3 and n is prime. In this paper, we prove Grüttmüller's conjecture for k = 2 and k = 3 by establishing a more general result for Cayley tables of Abelian groups of odd order.
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- Title
- Completing partial transversals of Cayley tables of Abelian groups
- Publication Details
- The Electronic Journal of Combinatorics, Vol.28(3), P3.60
- Resource Type
- Journal article
- Publisher
- Electronic Journal of Combinatorics; United States
- Series
- 28
- Copyright
- ©The authors.
- Identifiers
- WOS:000701859000004; 99380090776606600
- Academic Unit
- Mathematics and Statistics; Hal Marcus College of Science and Engineering
- Language
- English