In argumentation theory, Dung’s abstract framework provides a unifying view of several alternative semantics based on the notion of extension. Recently, a new semantics has been introduced to solve the problems related to counterintuitive results produced by literature proposals. In this semantics, extensions can be decomposed and constructed along the strongly connected components of the defea...

We construct twelve infinite families of pseudocyclic and non-amorphic association schemes, in which each nontrivial relation is a strongly regular graph. Three of the twelve families generalize the counterexamples to A. V. Ivanov’s conjecture by Ikuta and Munemasa [13].

Rival and Zaguia showed that the antichain cutsets of a finite Boolean lattice are exactly the level sets. We show that a similar characterization of antichain cutsets holds for any strongly connected poset of locally finite height. As a corollary, we characterize the antichain cutsets in semimodular lattices, supersolvable lattices, Bruhat orders, locally shellable lattices, and many more. We ...

A block negacyclic Bush-type Hadamard matrix of order 36 is used in a symmetric BGW(26, 25, 24) with zero diagonal over a cyclic group of order 12 to construct a twin strongly regular graph with parameters v=936, k=375, l=m=150 whose points can be partitioned in 26 cocliques of size 36. The same Hadamard matrix then is used in a symmetric BGW(50, 49, 48) with zero diagonal over a cyclic group o...

We construct two-intersection sets in PG(5, q), q odd, admitting PSL(2, q), whose associated strongly regular graphs have the same parameters as, but are not isomorphic to, Paley graphs.

Article history: Received 1 October 2012 Received in revised form 9 February 2015 Accepted 10 February 2015 Available online 14 February 2015

In [5], Holroyd, Levine, Mészáros, Peres, Propp and Wilson characterize recurrent chip-and-rotor configurations for strongly connected digraphs. However, the number of steps needed to recur, and the number of orbits is left open for general digraphs. Recently, these questions were answered by Pham [6], using linear algebraic methods. We give new, purely combinatorial proofs for these formulas. ...

We study multivariate entire functions and polynomials with non-negative coefficients. A class of Strongly Log-Concave entire functions, generalizingMinkowski volume polynomials, is introduced: an entire function f in m variables is called Strongly Log-Concave if the function (∂x1) c1 ...(∂xm) mf is either zero or log((∂x1) c1 ...(∂xm) mf) is concave on R + . We start with yet another point of ...