Association schemes of affine type over finite rings.
Associative graph products and their independence, domination and coloring numbers
Associative products are defined using a scheme of Imrich & Izbicki [18]. These include the Cartesian, categorical, strong and lexicographic products, as well as others. We examine which product ⊗ and parameter p pairs are multiplicative, that is, p(G⊗H) ≥ p(G)p(H) for all graphs G and H or p(G⊗H) ≤ p(G)p(H) for all graphs G and H. The parameters are related to independence, domination and irredundance. This includes Vizing's conjecture directly, and indirectly the Shannon capacity of a graph...
Associative Products of Graphs.
Asteroidal Quadruples in non Rooted Path Graphs
A directed path graph is the intersection graph of a family of directed subpaths of a directed tree. A rooted path graph is the intersection graph of a family of directed subpaths of a rooted tree. Rooted path graphs are directed path graphs. Several characterizations are known for directed path graphs: one by forbidden induced subgraphs and one by forbidden asteroids. It is an open problem to find such characterizations for rooted path graphs. For this purpose, we are studying in this paper directed...
Asymptotic analysis of Ramanujan pairs.
Asymptotic analysis of Ramanujan pairs. (Short Communication).
Asymptotic behavior of Pascal's triangle modulo a prime
Asymptotic behaviour of the simple random walk on the 2-dimensional comb.
Asymptotic bounds for bipartite Ramsey numbers.
Asymptotic comparison of two constructions for large digraphs of given degree and diameter
We compare the asymptotic growth of the order of the digraphs arising from a construction of Comellas and Fiol when applied to Faber-Moore digraphs versus plainly the Faber-Moore digraphs for the corresponding degree and diameter.
Asymptotic density in combined number systems.
Asymptotic enumeration of dense 0-1 matrices with equal row sums and equal column sums.
Asymptotic enumeration of labelled graphs by genus.
Asymptotic equipartition properties for simple hierarchical and networked structures
We prove asymptotic equipartition properties for simple hierarchical structures (modelled as multitype Galton-Watson trees) and networked structures (modelled as randomly coloured random graphs). For example, for large n, a networked data structure consisting of n units connected by an average number of links of order n / log n can be coded by about H × n bits, where H is an explicitly defined entropy. The main technique in our proofs are large deviation principles for suitably defined empirical...
Asymptotic equipartition properties for simple hierarchical and networked structures
We prove asymptotic equipartition properties for simple hierarchical structures (modelled as multitype Galton-Watson trees) and networked structures (modelled as randomly coloured random graphs). For example, for large n, a networked data structure consisting of n units connected by an average number of links of order n / log n can be coded by about H × n bits, where H is an explicitly defined entropy. The main technique in our proofs are large deviation principles for suitably defined empirical...
Asymptotic evolution of acyclic random mappings.
Asymptotic expansion of the equipoise curve of a polynomial inequality.
Asymptotic expansions for the coefficients of analytic generating functions.
Asymptotic expansions of certain sums involving powers of binomial coefficients.
Asymptotic form for generalized factorial