Two partial orders P = (X, S) and Q = (X, s’) are complementary if P fl Q = {(x, x): x E x} and the transitive closure of P U Q is {(x. y): x, y E X}. We investigate here the size w(n) of the largest set of pairwise complementary par!iai orders on a set of size n. In particular, for large n we construct L?(n/iogrt) mutually complementary partial orders of order n, and show on the other hand tha...

In this paper are introduced some concepts of interval-valued fuzzy relations and some of their properties: reflexivity, symmetry, T-transitivity, composition and local reflexivity. The existence and uniqueness of T-transitive closure of interval-valued fuzzy relations is proved. An algorithm to compute the T-transitive closure of finite interval-valued fuzzy relations is showed. Some propertie...

Shortest transitive edge relation presents an alternative to transitive closure relation for answering a class of complex biological queries that requires connectivity information but not the full transitive closure. A biological querie such “ find each downstream protein interacting with glutamine synthetase using five or fewer interactions ” does not require transitive closure. Shortest trans...

Abstract: An approach to calculate the exact transitive closure of a parameterized and normalized affine integer tuple relation is presented. A relation is normalized when it describes graphs of the chain topology only. A procedure of the normalization is attached. The exact transitive closure calculation is based on resolving a system of recurrence equations being formed from the input and out...

(g, x) → gx : G × X → X such that ex = x for every x in X and g(hx) = (gh)x for g and h in G and x in X (here e denotes the neutral element of G). It is easily seen that for each g in G the map x → gx is a homeomorphism of X whose inverse is the map x → g−1x . If x belongs to X and U is a subset of G, then U x = {gx : g ∈ U}. The action of G on X is transitive if Gx = X for every x in X . It is...

We show that the lexicographically least word in the orbit closure of the Rudin-Shapiro word w is 0w.

We compare three approaches to the notion of conjugacy for semigroups, the first one via the transitive closure of the uv ∼ vu relation, the second one via an action of inverse semigroups on themselves by partial transformations, and the third one via characters of finitedimensional representations.

We present a new transitive closure algorithm that is based on strong component detection. The new algorithm is more eecient than the previous transitive closure algorithms that are based on strong components detection, since it does not generate unnecessary partial successor sets and scans the input graph only once.