2012/07/09 by Behrooz Bagheri Gh., Gh., Behrooz Bagheri, Diane Donovan +3
Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1207.1969
openalex publication_date 2012/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A \sf μ-way Latin trade of volume s is a collection of μ partial Latin squares T1,T2,...,Tμ, 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 squares, and such that row i in each of the μ partial Latin squares contains, set-wise, the same symbols and column j, likewise. %If μ=2, (T1,T2) is called a \sf Latin bitrade. It is called \sf μ-way k-homogeneous Latin trade, if in each row and each column Tr, for 1≤ r≤ μ, contains exactly k elements, and each element appears in Tr exactly k times. It is also denoted by (μ,k,m) Latin trade,where m is the size of partial Latin squares. We introduce some general constructions for μ-way k-homogeneous Latin trades and specifically show that for all k ≤ m, 6≤ k ≤ 13 and k=15, and for all k ≤ m, k = 4, 5 (except for four specific values), a 3-way k-homogeneous Latin trade of volume km exists. We also show that there are no (3,4,6) Latin trade and (3,4,7) Latin trade. Finally we present general results on the existence of 3-way k-homogeneous Latin trades for some modulo classes of m.