86,822 research outputs found
Representation of finite graphs as difference graphs of S-units, I
In part I of the present paper the following problem was investigated. Let G be a finite simple graph, and S be a finite set of primes. We say that G is representable with S if it is possible to attach rational numbers to the vertices of G such that the vertices v_1,v_2 are connected by an edge if and only if the difference of the attached values is an S-unit. In part I we gave several results concerning the representability of graphs in the above sense.In the present paper we extend the results from paper I to the algebraic number field case and make some of them effective. Besides we prove some new theorems: we prove that G is infinitely representable with S if and only if it has a degenerate representation with S, and we also deal with the representability with S of the union of two graphs of which at least one is finitely representable with S.p, li { white-space: pre-wrap; }</style
On conjectures and problems of Ruzsa concerning difference graphs of S-units
Given a finite nonempty set of primes S, we build a graph with
vertex set by connecting x and y if the prime divisors of both the
numerator and denominator of x-y are from S. In this paper we resolve two
conjectures posed by Ruzsa concerning the possible sizes of induced
nondegenerate cycles of , and also a problem of Ruzsa concerning
the existence of subgraphs of which are not induced subgraphs.Comment: 15 page
Finite Dimension: A Mathematical Tool to Analise Glycans
There is a need to develop widely applicable tools to understand glycan organization, diversity and structure. We present a graph-theoretical study of a large sample of glycans in terms of finite dimension, a new metric which is an adaptation to finite sets of the classical Hausdorff "fractal" dimension. Every glycan in the sample is encoded, via finite dimension, as a point of Glycan Space, a new notion introduced in this paper. Two major outcomes were found: (a) the existence of universal bounds that restrict the universe of possible glycans and show, for instance, that the graphs of glycans are a very special type of chemical graph, and (b) how Glycan Space is related to biological domains associated to the analysed glycans. In addition, we discuss briefly how this encoding may help to improve search in glycan databases.Fil: Alonso, Juan Manuel. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias FÃsico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; ArgentinaFil: Arroyuelo, Agustina. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias FÃsico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; ArgentinaFil: Garay, Pablo Germán. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias FÃsico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; ArgentinaFil: MartÃn, Osvaldo Antonio. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias FÃsico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; ArgentinaFil: Vila, Jorge Alberto. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias FÃsico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentin
The Noncommutative Geometry of k-graph C*-Algebras
This paper is comprised of two related parts. First we discuss which k-graph
algebras have faithful gauge invariant traces, where the gauge action of \T^k
is the canonical one. We give a sufficient condition for the existence of such
a trace, identify the C*-algebras of k-graphs satisfying this condition up to
Morita equivalence, and compute their K-theory.
For k-graphs with faithful gauge invariant trace, we construct a smooth
-summable semifinite spectral triple. We use the semifinite local
index theorem to compute the pairing with K-theory. This numerical pairing can
be obtained by applying the trace to a KK-pairing with values in the K-theory
of the fixed point algebra of the \T^k action. As with graph algebras, the
index pairing is an invariant for a finer structure than the isomorphism class
of the algebra.Comment: 38 pages, some pictures drawn in picTeX Some minor technical
revisions. Material has been reorganised with detailed discussion of k-graphs
admitting graph traces shortened and moved to an appendix. This version to
appear in K-theor
Realizations of AF-algebras as graph algebras, Exel-Laca algebras, and ultragraph algebras
We give various necessary and sufficient conditions for an AF-algebra to be
isomorphic to a graph C*-algebra, an Exel-Laca algebra, and an ultragraph
C*-algebra. We also explore consequences of these results. In particular, we
show that all stable AF-algebras are both graph C*-algebras and Exel-Laca
algebras, and that all simple AF-algebras are either graph C*-algebras or
Exel-Laca algebras. In addition, we obtain a characterization of AF-algebras
that are isomorphic to the C*-algebra of a row-finite graph with no sinks.Comment: 34 pages, Version 2 comments: Some minor typos corrected; Version 3
comments: Some typos corrected. This is the version to appea
The QCD deconfinement transition for heavy quarks and all baryon chemical potentials
Using combined strong coupling and hopping parameter expansions, we derive an
effective three-dimensional theory from thermal lattice QCD with heavy Wilson
quarks. The theory depends on traced Polyakov loops only and correctly reflects
the centre symmetry of the pure gauge sector as well as its breaking by finite
mass quarks. It is valid up to certain orders in the lattice gauge coupling and
hopping parameter, which can be systematically improved. To its current order
it is controlled for lattices up to N_\tau\sim 6 at finite temperature. For
nonzero quark chemical potentials, the effective theory has a fermionic sign
problem which is mild enough to carry out simulations up to large chemical
potentials. Moreover, by going to a flux representation of the partition
function, the sign problem can be solved. As an application, we determine the
deconfinement transition and its critical end point as a function of quark mass
and all chemical potentials.Comment: 24 pages, 17 figure
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