Generalized Right Angular Designs

Generalized packing designs

Generalized t-designs, which form a common generalization of objects such as tdesigns, resolvable designs and orthogonal arrays, were defined by Cameron [P.J. Cameron, A generalisation of t-designs, Discrete Math. 309 (2009), 4835–4842]. In this paper, we define a related class of combinatorial designs which simultaneously generalize packing designs and packing arrays. We describe the sometimes...

Generalized whist tournament designs

In this study a new class of tournament designs is introduced. In particular, each game of the tournament involves several (two or more) teams competing against one another. The tournament is also required to satisfy certain balance conditions that are imposed on each pair of players. These balance conditions are related to both the total number of players on each team and the number of teams i...

Generalized orthogonal designs

Generalized Resolution and Minimum Aberration for Nonregular Fractional Factorial Designs

Seeking the optimal design with a given number of runs is a main problem in fractional factorial designs(FFDs). Resolution of a design is the most widely usage criterion, which is introduced by Box and Hunter(1961), used to be employed to regular FFDs. The resolution criterion is extended to non-regular FFG, called the generalized resolution criterion. This criterion is providing the idea of ge...

Generalized Weisner Designs and Quasigroups

An n-ary quasigroup (Q, A) such that for some i ∈ {1, . . . , n} the identity A(A(x1 ), A(x n−1 2 , x1), . . . , A(xn, x n−1 1 )) = xi holds is called an i-Weisner n-quasigroup ( i-W-n-quasigroup ). iW-nquasigroups represent a generalization of quasigroups satisfying Schröder law (xy · yx = x) and quasigroups satisfying Stein’s third law (xy · yx = y). Properties of i-W-n-quasigroups which are ...