A perfect binary array is an r-dimensional array with elements k 1 such that all out-of-phase periodic autocorrelation coefficients are zero. Such an array is equivalent to a Menon difference set in an abelian group. We give recursive constructions for four infinite families of two-dimensional perfect binary arrays, using only elementary methods. Brief outlines of the proofs were previously giv...

We investigate perfect codes in Zn in the `p metric. Upper bounds for the packing radius r of a linear perfect code in terms of the metric parameter p and the dimension n are derived. For p = 2 and n = 2, 3, we determine all radii for which there exist linear perfect codes. The non-existence results for codes in Zn presented here imply non-existence results for codes over finite alphabets Zq, w...

Let h be a connective homology theory. We construct functorial relative plus construction as Bousfield localization functor in the category of maps spaces. It allows us to associate pair (X,H), consisting connected space X and an h-perfect normal subgroup H fundamental group π1(X), h-acyclic map X→XH+h inducing quotient by on group. show that this is terminal among kill H. When ordinary theory ...

A minimal blocker in a bipartite graph G is a minimal set of edges the removal of which leaves no perfect matching in G. We give a polynomial delay algorithm for finding all minimal blockers of a given bipartite graph. Equivalently, this gives a polynomial delay algorithm for listing the anti-vertices of the perfect matching polytope P (G) = {x ∈ R | Hx = e, x ≥ 0}, where H is the incidence mat...

After having rejected the so-called Anteriority Theories of the Perfect tense which are based on the Reichenbachian E-R,S and E-R-S schemes where E-R is to be taken as expressing the earlier than relation E<R, the author argues in favour of a tense theory in which the notion of the Extended Now (EN) plays a dominant role. She also rejects theories in which the Perfect is analyzed syncategoremat...

The Strong Perfect Graph Conjecture, suggested by Claude Berge in 1960, had a major impact on the development of graph theory over the last forty years. It has led to the definitions and study of many new classes of graphs for which the Strong Perfect Graph Conjecture has been verified. Powerful concepts and methods have been developed to prove the Strong Perfect Graph Conjecture for these spec...

In this paper we give a characterization of kernel-perfect (and of critical kernel-imperfect) arc-local tournament digraphs. As a consequence, we prove that arc-local tournament digraphs satisfy a strenghtened form of the following interesting conjecture which constitutes a bridge between kernels and perfectness in digraphs, stated by C. Berge and P. Duchet in 1982: a graph G is perfect if and ...

In this article, we present a characterization of basic graphs in terms of forbidden induced subgraphs. This class of graphs was introduced by Conforti, Cornuéjols and Vušković [3], and it plays an essential role in the announced proof of the Strong Perfect Graph Conjecture by Chudnovsky, Robertson, Seymour and Thomas [2]. Then we apply the Reducing Pseudopath Method [13] to characterize the su...

In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple designs are also useful in other constructions, such as superimposed codes and perfect hash families etc. The existence of super-simple (v, 4, λ)-BIBDs have been determined for λ = 2, 3, 4 and 6. When λ = 5, the necessary conditions of such a d...