Cavenagh and Wanless [Discrete Appl. Math. 158 no. 2 (2010), 136–146] determined the possible intersection of any two transversals of the back circulant latin square Bn, and used the result to completely determine the spectrum for 2-way k-homogeneous latin trades. We generalize this problem to the intersection of μ transversals of Bn such that the transversals intersect stably (that is, the int...

The Poggendorff illusion was approached with a novel perspective, that of applying Emmert's Law to the situation. The extensities between the verticals and the transversals happen to be absolutely equal in retinal image size, whereas the registered distance for the verticals must be smaller than that of the transversals due to the fact that the former is assumed to occlude the latter. This comb...

Given any system of n subsets in a matroid M , a transversal of this system is an n-tuple of elements of M , one from each set, which is independent. Two transversals differing by exactly one element are adjacent, and two transversals connected by a sequence of adjacencies are locally equivalent, the distance between them being the minimum number of adjacencies in such a sequence. We give two s...

We consider a generalization of the notion of transversal to a finite hypergraph, so called weighted transversals. Given a non-negative weight vector assigned to each hyperedge of the input hypergraph, we define a weighted transversal as a minimal vertex set which intersects a collection of hyperedges of sufficiently large total weight. We show that the hypergraph of all weighted transversals i...

In this paper, we consider another generalization for quasi-ideal orthodox transversal, the so-called S0-orthodox transversals. We give a structure theorem for regular semigroups with S0-orthodox transversals. If S0 is a S0-orthodox transversal of S then S can be described in terms of S0. Mathematics Subject Classification: 20M10

We construct three (large, reduced) incidence algebras whose semigroups of multiplicative functions, under convolution, are anti-isomorphic, respectively, to the semigroups of what we call partitional, permutational and exponential formal power series without constant term, in infinitely many variables x = (x,, x2,...), under plethysm. We compute the Mobius function in each case. These three in...

Some properties and characterizations for abundant semigroups with generalised quasiadequate transversals are explored. In such semigroups, an interesting property [?a,b ? Re1S, VSo(a) VSo (b) 0 (a) = (b)] is investigated thus the concept of refined quasi-adequate transversals, short, RGQA introduced. It shown that real common generalisations both orthodox adequate in case. Finally, by means tw...

We generalize the Hadwiger(-Danzer-Grünbaum-Klee) theorem on line transversals for an unbounded family of compact convex sets to the case of transversal planes of arbitrary dimension. This is the first Helly-type theorem known for transversals of dimension between 1 and d− 1.