It is known that a graded lattice of rank n is supersolvable if and only if it has an EL-labelling where the labels along any maximal chain are exactly the numbers 1, 2, . . . , n without repetition. These labellings are called Sn EL-labellings, and having such a labelling is also equivalent to possessing a maximal chain of left modular elements. In the case of an ungraded lattice, there is a n...

This paper proposes a bi-objective reliable supply chain network design that immunizes the network against different sources of uncertainties. In this regard, scenario based stochastic programming method is applied to model different disruption scenarios affecting accurate performance of network stages. Also, reliable and unreliable facilities are suggested for lessening vulnerability of networ...

We analyze random walks on a class of semigroups called “leftregular bands”. These walks include the hyperplane chamber walks of Bidigare, Hanlon, and Rockmore. Using methods of ring theory, we show that the transition matrices are diagonalizable and we calculate the eigenvalues and multiplicities. The methods lead to explicit formulas for the projections onto the eigenspaces. As examples of th...

The Tamari lattice Tn was originally defined on bracketings of a set of n+1 objects, with a cover relation based on the associativity rule in one direction. Although in several related lattices, the number of maximal chains is known, quoting Knuth, “The enumeration of such paths in Tamari lattices remains mysterious.” The lengths of maximal chains vary over a great range. In this paper, we focu...

During the last decade, CCS has been extended in different directions, among them priority and real time. One of the most satisfactory results for CCS is Milner’s complete proof system for observational congruence [?]. Observational congruence is fair in the sense that it is possible to escape divergence, reflected by an axiom recX.(τ.X + P ) = recX.τ.P . In this paper we discuss observational ...

A model for statistical ranking is a family of probability distributions whose states are orderings of a fixed finite set of items. We represent the orderings as maximal chains in a graded poset. The most widely used ranking models are parameterized by rational function in the model parameters, so they define algebraic varieties. We study these varieties from the perspective of combinatorial co...

We study chains in an H-closed topological partially ordered space. We give sufficient conditions for a maximal chain L in an H-closed topological partially ordered space such that L contains a maximal (minimal) element. Also we give sufficient conditions for a linearly ordered topological partially ordered space to be H-closed. We prove that any H-closed topological semilattice contains a zero...

Given a graph G = (V,E) and a proper vertex colouring of G, a Kempe chain is a subset of V that induces a maximal connected subgraph of G in which every vertex has one of two colours. To make a Kempe change is to obtain one colouring from another by exchanging the colours of vertices in a Kempe chain. Two colourings are Kempe equivalent if each can be obtained from the other by a series of Kemp...

During the last decade, CCS has been extended in diier-ent directions, among them priority and real time. One of the most satisfactory results for CCS is Milner's complete proof system for observational congruence 28]. Observational congruence is fair in the sense that it is possible to escape divergence, reeected by an axiom recX:(:X + P) = recX:::P. In this paper we discuss observational cong...