We examine the problem of finite-state representability of infinitestate processes w.r.t. certain behavioural equivalences. We show that the classical notion of regularity becomes insufficient in case of all equivalences of van Glabbeek’s hierarchy except bisimilarity, and we design and justify a generalization in the form of strong regularity and finite characterizations. We show that the cond...

We show for many strongly regular graphs ∆, and for all Taylor graphs ∆ except the hexagon, that locally ∆ graphs have bounded diameter.

An n-tournament is an orientation of a complete n-partite graph. It was proved by J.A. Bondy in 1976 that every strongly connected n-partite tournament has an n-cycle. We characterize strongly connected n-partite tournaments in which a longest cycle is of length n and, thus, settle a problem in L. Volkmann, Discrete Math. 245 (2002) 19-53.

This paper begins the project of adapting the 1992 book by Adams, Barbasch and Vogan on the Langlands classification of admissible representations of real groups, to padic groups, continuing in the direction charted by Vogan in his 1993 paper on the Langlands correspondence. This paper presents three theorems in that direction. The first theorem shows how Lusztig’s work on perverse sheaves aris...

A quasi-symmetric design (QSD) is a (v, k, λ) design with two intersection numbers x, y, where 0 ≤ x < y < k. The block graph of a QSD is a strongly regular graph (SRG), whereas the converse is not true. Using Neumaier’s classification of SRGs related to the smallest eigenvalue, a complete parametric classification of QSDs whose block graph is an SRG with smallest eigenvalue −3, or second large...

If a1, . . . , ak and n are positive integers such that n = a1 + · · · + ak, then the tuple (a1, . . . , ak) is a composition of n of length k. We say that (a1, . . . , ak) strongly t-intersects (b1, . . . , bk) if there are at least t distinct indices i such that ai = bi. A set A of compositions is strongly t-intersecting if every two members of A strongly t-intersect. Let Cn,k be the set of a...