A partial difference set having parameters (n2, r(n− 1), n+ r2 − 3r, r2 − r) is called a Latin square type partial difference set, while a partial difference set having parameters (n2, r(n+1),−n+r2+3r, r2+r) is called a negative Latin square type partial difference set. Nearly all known constructions of negative Latin square partial difference sets are in elementary abelian groups. In this pape...

We show that for all integers m > 4 there exists a 2m × 2m ×m latin cuboid that cannot be completed to a 2m × 2m × 2m latin cube. We also show that for all even m / ∈ {2, 6} there exists a (2m−1) × (2m−1) × (m−1) latin cuboid that cannot be extended to any (2m−1)× (2m−1)×m latin cuboid.

"Assessing the Impact of Computer-Assisted Instruction (CAI) in Undergraduate Latin American Studies Courses"1 by Jack Child, Professor of Spanish and Latin American Studies, The American University, Washington, DC. Prepared for panel "Computers in Latin American Literature and Culture", XIXth International Congress of the Latin American Studies Association, Washington, DC, September 1995 (This...

IsotoIHsl:n that lower bounds for infinite N of order n. hand or computer, strong critical sets of minimum nOn-lS01110Tnitnc reduced latin squares of order less than or of order 6. These latin squares have been taken from 129 onwards. We summarise our results in Table the numbering system listed by Denes and Keedwell latin squares. This numbering system is based on the ,<:n,,-r1i',rrHl1<:rn cla...

A μ-way k-homogeneous Latin trade was defined by Bagheri Gh, Donovan, Mahmoodian (2012), where the existence of 3-way k-homogeneous Latin trades was specifically investigated. We investigate the existence of a certain class of μ-way k-homogeneous Latin trades with an idempotent like property. We present a number of constructions for μ-way k-homogeneous Latin trades with this property, and show ...

A comparison between the performance of Latin and Arabic handwritten digits recognition problems is presented. The performance of ten different classifiers is tested on two similar Arabic and Latin handwritten digits databases. The analysis shows that Arabic handwritten digits recognition problem is easier than that of Latin digits. This is because the interclass difference in case of Latin dig...

It is known that t mutually orthogonal latin squares of order n generate a b t 2c-error correcting code with n codewords. In this paper we consider latin squares of order n made up of elements taken from Zn. In this situation we consider when this code is linear. We present neccessary and sufficient conditions on the latin squares and obtain a method of constructing a maximal family of mutually...

Orthogonal latin squares of Sudoku type Hans-Dietrich Gronau Universität Rostock, Inst. für Mathematik 18051 Rostock, Germany We present results on the existence of orthogonal latin squares and latin rectangles of Sudoku type.

Spatially Balanced Latin Squares are combinatorial structures of great importance for experimental design. From a computational perspective they present a challenging problem and there is a need for efficient methods to generate them. Motivated by a real-world application, we consider a natural extension to this problem, balanced Latin Rectangles. Balanced Latin Rectangles appear to be even mor...

Symmetries of a partial Latin square are primarily determined by its autotopism group. Analogously to the case of Latin squares, given an isotopism Θ, the cardinality of the set PLSΘ of partial Latin squares which are invariant under Θ only depends on the conjugacy class of the latter, or, equivalently, on its cycle structure. In the current paper, the cycle structures of the set of autotopisms...