1,744 research outputs found
Factorization Properties of Leamer Monoids
The Huneke-Wiegand conjecture has prompted much recent research in
Commutative Algebra. In studying this conjecture for certain classes of rings,
Garc\'ia-S\'anchez and Leamer construct a monoid S_\Gamma^s whose elements
correspond to arithmetic sequences in a numerical monoid \Gamma of step size s.
These monoids, which we call Leamer monoids, possess a very interesting
factorization theory that is significantly different from the numerical monoids
from which they are derived. In this paper, we offer much of the foundational
theory of Leamer monoids, including an analysis of their atomic structure, and
investigate certain factorization invariants. Furthermore, when S_\Gamma^s is
an arithmetical Leamer monoid, we give an exact description of its atoms and
use this to provide explicit formulae for its Delta set and catenary degree
Weakly directed self-avoiding walks
We define a new family of self-avoiding walks (SAW) on the square lattice,
called weakly directed walks. These walks have a simple characterization in
terms of the irreducible bridges that compose them. We determine their
generating function. This series has a complex singularity structure and in
particular, is not D-finite. The growth constant is approximately 2.54 and is
thus larger than that of all natural families of SAW enumerated so far (but
smaller than that of general SAW, which is about 2.64). We also prove that the
end-to-end distance of weakly directed walks grows linearly. Finally, we study
a diagonal variant of this model
Minimal reducible bounds for induced-hereditary properties
AbstractLet (Ma,⊆) and (La,⊆) be the lattices of additive induced-hereditary properties of graphs and additive hereditary properties of graphs, respectively. A property R∈Ma (∈La) is called a minimal reducible bound for a property P∈Ma (∈La) if in the interval (P,R) of the lattice Ma (La) there are only irreducible properties. The set of all minimal reducible bounds of a property P∈Ma in the lattice Ma we denote by BM(P). Analogously, the set of all minimal reducible bounds of a property P∈La in La is denoted by BL(P).We establish a method to determine minimal reducible bounds for additive degenerate induced-hereditary (hereditary) properties of graphs. We show that this method can be successfully used to determine already known minimal reducible bounds for k-degenerate graphs and outerplanar graphs in the lattice La. Moreover, in terms of this method we describe the sets of minimal reducible bounds for partial k-trees and the graphs with restricted order of components in La and k-degenerate graphs in Ma
Random Surfing Without Teleportation
In the standard Random Surfer Model, the teleportation matrix is necessary to
ensure that the final PageRank vector is well-defined. The introduction of this
matrix, however, results in serious problems and imposes fundamental
limitations to the quality of the ranking vectors. In this work, building on
the recently proposed NCDawareRank framework, we exploit the decomposition of
the underlying space into blocks, and we derive easy to check necessary and
sufficient conditions for random surfing without teleportation.Comment: 13 pages. Published in the Volume: "Algorithms, Probability, Networks
and Games, Springer-Verlag, 2015". (The updated version corrects small
typos/errors
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