Construction of Symmetric Balanced Squares with Blocksize More than One |
| |
Authors: | Palash Sarkar Paul J Schellenberg |
| |
Institution: | (1) Applied Statistics Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata, 700108, India;(2) Department of Combinatorics and Optimization, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada, N2L 3G1 |
| |
Abstract: | In this paper we study a generalization of symmetric latin squares. A symmetric balanced square of order v, side s and blocksize k is an s×s symmetric array of k-element subsets of {1,2,..., v} such that every element occurs in ks/v or ks/v cells of each row and column. every element occurs in ks2/v or ks
2
v cells of the array. Depending on the values s, k and v, the problem naturally divides into three subproblems: (1) v ks (2) s < v < ks (3) v s. We completely solve the first problem and we recursively reduce the third problem to the first two. For s 4 we provide direct constructions for the second problem. Moreover, we provide a general construction method for the second problem utilizing flows in a network. We have been able to show the correctness of this construction for k 3. For k 4, the problem remains open. |
| |
Keywords: | symmetric Latin square combinatorial design symmetric balanced square min cut-max flow theorem |
本文献已被 SpringerLink 等数据库收录! |
|