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On the existence of Κ-homogeneous Latin bitrades

Bagheri Gh., B ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. Publisher: 2011
  3. Abstract:
  4. Let T be a partial Latin square and L a Latin square such that T ⊆ L.Then T is called a Latin trade, if there exists a partial Latin square T * such that T* ∩ T = ∅ and (LT) ∪ T* is a Latin square.We call T* a disjoint mate of T and the pair (T,T*) is called a Latin itrade.A Latin bitrade where empty rows and columns are ignored, is called a Κ-homogeneous Latin bitrade, if in each row and each column it contains exactly κ elements, and each element appears exactly k times.The number of filled cells in a Latin trade is referred to as its volume.Following the earlier work on κ-homogeneous Latin bitrades by Cavenagh, Donovan, and Drápal (2003 and 2004) Bean, Bidkhori, Khosravi, and E.S.Mahmoodian (2005) we provethe following re-sults.All κ-homogeneous Latin bitrades of volume km exist, for all odd integers κ and m > k. all even integers κ > 2 and m > min{fc + u, 3k/2}, where u is any odd integer which divides k. all m > k, where 3 < k < 37
  5. Keywords:
  6. Homogeneous Latin bitrades ; Latin trades ; Volume of Latin bitrades
  7. Source: Utilitas Mathematica ; Volume 85 , 2011 , Pages 333-345 ; 03153681 (ISSN)