On the possible volumes of mu-way latin trades

Adams, P., Billington, E. J., Bryant, D. E. and Mahmoodian, E. (2002) On the possible volumes of mu-way latin trades. Aequationes Mathematicae, 63 3: 303-320.


Author Adams, P.
Billington, E. J.
Bryant, D. E.
Mahmoodian, E.
Title On the possible volumes of mu-way latin trades
Formatted title
On the possible volumes of ¹-way latin trades
Journal name Aequationes Mathematicae   Check publisher's open access policy
ISSN 0001-9054
Publication date 2002
Volume 63
Issue 3
Start page 303
End page 320
Total pages 18
Editor Reich, L. A.
Gronau, D.
Place of publication Switzerland
Publisher Birkhaeuser Verlag AG
Collection year 2002
Subject C1
230101 Mathematical Logic, Set Theory, Lattices And Combinatorics
780101 Mathematical sciences
010107 Mathematical Logic, Set Theory, Lattices and Universal Algebra
01 Mathematical Sciences
Formatted abstract
A ¹-way latin trade of volume s is a set of ¹ partial latin rectangles (of inconsequential
size) containing exactly the same s ¯lled cells, such that if cell (i; j) is ¯lled, it contains a di®erent
entry in each of the ¹ partial latin rectangles, and such that row i in each of the ¹ partial latin
rectangles contains, set-wise, the same symbols and column j, likewise. In this paper we show
that all ¹-way latin trades with su±ciently large volumes exist, and state some theorems on the
non-existence of ¹-way latin trades of certain volumes. We also ¯nd the set of possible volumes
(that is, the volume spectrum) of ¹-way latin trades for ¹ = 4 and 5. (The case ¹ = 2 was dealt
with by Fu, and the case ¹ = 3 by the present authors.)
Q-Index Code C1

 
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Created: Tue, 14 Aug 2007, 17:06:39 EST