Large sets of resolvable idempotent Latin squares

An idempotent Latin square of order v is called resolvable and denoted by RILS(v) if the v(v-1) off-diagonal cells can be resolved into v-1 disjoint transversals. A large set of resolvable idempotent Latin squares of order v, briefly LRILS(v), is a collection of v-2 RILS(v)s pairwise agreeing on only the main diagonal. In this paper we display some recursive and direct constructions for LRILSs.

[1]  Luc Teirlinck,et al.  Some new 2-resolvable Steiner quadruple systems , 1994, Des. Codes Cryptogr..

[2]  Yanxun Chang,et al.  Product constructions for large sets of resolvable MTSs and DTSs , 2005, Australas. J Comb..

[3]  Shengyuan Zhang,et al.  An improved product construction for large sets of Kirkman triple systems , 2003, Discret. Math..

[4]  Hongtao Zhao,et al.  More large sets of resolvable MTS and resolvable DTS with odd orders , 2008, Discret. Math..

[5]  Lijun Ji,et al.  Further results on large sets of Kirkman triple systems , 2008, Discret. Math..

[6]  Luc Teirlinck.  Large sets with holes , 1993 .

[7]  C. Colbourn,et al.  The CRC handbook of combinatorial designs , edited by Charles J. Colbourn and Jeffrey H. Dinitz. Pp. 784. $89.95. 1996. ISBN 0-8493-8948-8 (CRC). , 1997, The Mathematical Gazette.

[8]  Landang Yuan,et al.  Some infinite families of large sets of Kirkman triple systems , 2008 .

[9]  Landang Yuan,et al.  Another construction for large sets of Kirkman triple systems , 2008, Des. Codes Cryptogr..

[10]  Yanxun Chang.  The spectrum for large sets of idempotent quasigroups , 2000 .

[11]  C. Colbourn,et al.  Mutually orthogonal latin squares (MOLS) , 2006 .

[12]  Ronald D. Baker,et al.  Partitioning the planes of AG2m(2) into 2-designs , 1976, Discret. Math..

[13]  Hedvig Mohácsy,et al.  Candelabra systems and designs , 2002 .

[14]  Lijun Ji.  A construction for large sets of disjoint Kirkman triple systems , 2007, Des. Codes Cryptogr..

[15]  Charles C. Lindner.  On the Number of Disjoint Mendelsohn Triple Systems , 1981, J. Comb. Theory, Ser. A.

[16]  Charles C. Lindner,et al.  The Construction of Large Sets of Idempotent Quasigroups , 1988, Eur. J. Comb..