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On the possible volumes of μ-way latin trades

Adams, P ; Sharif University of Technology | 2002

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  1. Type of Document: Article
  2. DOI: 10.1007/s00010-002-8026-4
  3. Publisher: Birkhauser Verlag Basel , 2002
  4. Abstract:
  5. A μ-way latin trade of volume s is a set of μ partial latin rectangles (of inconsequential size) containing exactly the same s filled cells, such that if cell (i, j) is filled, it contains a different entry in each of the μ partial latin rectangles, and such that row i in each of the μ partial latin rectangles contains, set-wise, the same symbols and column j, likewise. In this paper we show that all μ-way latin trades with sufficiently large volumes exist, and state some theorems on the non-existence of μ-way latin trades of certain volumes. We also find the set of possible volumes (that is, the volume spectrum) of μ-way latin trades for μ = 4 and 5. (The case μ = 2 was dealt with by Fu, and the case μ = 3 by the present authors.). © Birkhäuser Verlag, Basel, 2002
  6. Keywords:
  7. Intersection ; Latin rectangle ; Latin square ; Trade ; Volume of trade
  8. Source: Aequationes Mathematicae ; Volume 63, Issue 3 , 2002 , Pages 303-320 ; 00019054 (ISSN)
  9. URL: https://link.springer.com/article/10.1007/s00010-002-8026-4