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On Normal Cayley graphs and Homidempotent graphs
, 2004
"... A graph G is said to be homidempotent if there is a homomorphism from G 2 to G, and weakly homidempotent if for some n ≥ 1 there is a homomorphism from G n+1 to G n. We characterise both classes of graphs in terms of a special class of Cayley graphs called normal Cayley graphs. This allows us to c ..."
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Cited by 3 (0 self)
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A graph G is said to be homidempotent if there is a homomorphism from G 2 to G, and weakly homidempotent if for some n ≥ 1 there is a homomorphism from G n+1 to G n. We characterise both classes of graphs in terms of a special class of Cayley graphs called normal Cayley graphs. This allows us
Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 546 (25 self)
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Least fixpoints as meanings of recursive definitions.
Gravity coupled with matter and the foundation of non commutative geometry
, 1996
"... We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element ds. Its unitary representations correspond to Riemannian metrics and Spin structure while ds is the Dirac propagator ds = ×— × = D −1 where D i ..."
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Cited by 354 (18 self)
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transformations appears spontaneously as a normal subgroup of the diffeomorphism group.
On the geometry and cohomology of some simple Shimura varieties
, 1999
"... This paper has twin aims. On the one hand we prove the local Langlands conjecture for GL n over a padic field. On the other hand in many cases we are able to identify the action of the decomposition group at a prime of bad reduction on the ladic cohomology of the "simple" Shimura varieti ..."
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Cited by 341 (19 self)
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This paper has twin aims. On the one hand we prove the local Langlands conjecture for GL n over a padic field. On the other hand in many cases we are able to identify the action of the decomposition group at a prime of bad reduction on the ladic cohomology of the "simple" Shimura varieties studied by Kottwitz in [Ko4]. These two problems go hand in hand. The local Langlands conjecture is one of those hydra like conjectures which seems to grow as it gets proved. However the generally accepted formulation seems to be the following (see [He2]). Let K be a finite extension of Q p . Fix a nontrivial additive character # : K
Graph homomorphisms: structure and symmetry
"... This paper is the first part of an introduction to the subject of graph homomorphism in the mixed form of a course and a survey. We give the basic definitions, examples and uses of graph homomorphisms and mention some results that consider the structure and some parameters of the graphs involved. We ..."
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Cited by 45 (2 self)
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. We discuss vertex transitive graphs and Cayley graphs and their rather fundamental role in some aspects of graph homomorphisms. Graph colourings are then explored as homomorphisms, followed by a discussion of various graph products.
Full Abstraction for PCF
 INFORMATION AND COMPUTATION
, 1996
"... An intensional model for the programming language PCF is described, in which the types of PCF are interpreted by games, and the terms by certain "historyfree" strategies. This model is shown to capture definability in PCF. More precisely, every compact strategy in the model is definable i ..."
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Cited by 254 (16 self)
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An intensional model for the programming language PCF is described, in which the types of PCF are interpreted by games, and the terms by certain "historyfree" strategies. This model is shown to capture definability in PCF. More precisely, every compact strategy in the model is definable in a certain simple extension of PCF. We then introduce an intrinsic preorder on strategies, and show that it satisfies some remarkable properties, such that the intrinsic preorder on function types coincides with the pointwise preorder. We then obtain an orderextensional fully abstract model of PCF by quotienting the intensional model by the intrinsic preorder. This is the first syntaxindependent description of the fully abstract model for PCF. (Hyland and Ong have obtained very similar results by a somewhat different route, independently and at the same time.) We then consider the effective version of our model, and prove a Universality Theorem: every element of the effective extensional model is definable in PCF. Equivalently, every recursive strategy is definable up to observational equivalence.
Reflection positivity, rank connectivity, and homomorphism of graphs
 Journal of the American Mathematical Society
"... It is shown that a graph parameter can be realized as the number of homomorphisms into a fixed (weighted) graph if and only if it satisfies two linear algebraic conditions: reflection positivity and exponential rankconnectivity. In terms of statistical physics, this can be viewed as a characterizat ..."
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Cited by 76 (25 self)
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It is shown that a graph parameter can be realized as the number of homomorphisms into a fixed (weighted) graph if and only if it satisfies two linear algebraic conditions: reflection positivity and exponential rankconnectivity. In terms of statistical physics, this can be viewed as a
Results 1  10
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1,742