Resolvable perfect Mendelsohn designs with block size five

Perfect Mendelsohn designs with block size six

Self-converse Mendelsohn designs with odd block size

A Mendelsohn design .M D(v, k,).) is a pair (X, B), where X is a vset together with a collection B of ordered k-tuples from X such that each ordered pair from X is contained in exactly ). k-tuples of B. An M D(v, k,).) is said to be self-converse, denoted by SC!'vf D( v, k,).) = (X,B,/), if there is an isomorphism / from (X, B) to (X,B), where B-1 {(Xk,:r:k-l, ... ,X2,Xl); (Xl,,,,,Xk) E B}. The...

Self-converse Mendelsohn designs with block size 6q

A Mendelsohn design lv! D( v, k, A) is a pair (X, B) where X is a v-set together with a collection B of cyclic k-tuples from X such that each ordered pair from X is contained in exactly A cyclic k-tuples of B. An M D(v, k, A) is said to be self-converse, denoted by SC1\ID(v,k,A) = (X,B,f), if there is an isomorphism f from (X, B) to (X, B-1), where B1 = {(:Ek,:r:k-l, ""X2,Xl!: (:1:1, ""Xk! E B}...

Resolvable group divisible designs with block size 3

A group divisible design is resolvable if there exists a partition n = {P,, Pz, . .} of p such that each part Pi is itself a partition of X. In this paper we investigate the existence of resolvable group divisible designs with K = {3}, M a singleton set, and all A. The case where M = { 1) has been solved by Ray-Chaudhuri and Wilson for I = 1, and by Hanani for all h > 1. The case where M is a s...

Resolvable Modified Group Divisible Designs with Block Size Three

A resolvable modified group divisible design (RMGDD) is an MGDD whose blocks can be partitioned into parallel classes. In this article, we investigate the existence of RMGDDs with block size three and show that the necessary conditions are also sufficient with two exceptions. # 2005 Wiley Periodicals, Inc. J Combin Designs 15: 2–14, 2007