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Explicit monomial expansions of the generating series for connection coefficients. ArXiv:1111.6215, 2011. Olivier Bernardi Department of Mathematics, Massachusetts Institute of Technology; Cambridge, MA USA 02139 bernardi@math.mit.edu Rosena R
"... Abstract. This paper is devoted to the explicit computation of generating series for the connection coefficients of two commutative subalgebras of the group algebra of the symmetric group, the class algebra and the double coset algebra. As shown by Hanlon, Stanley and Stembridge (1992), these series ..."
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Cited by 4 (0 self)
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Abstract. This paper is devoted to the explicit computation of generating series for the connection coefficients of two commutative subalgebras of the group algebra of the symmetric group, the class algebra and the double coset algebra. As shown by Hanlon, Stanley and Stembridge (1992), these series gives the spectral distribution of some random matrices that are of interest to statisticians. Morales and Vassilieva (2009, 2011) found explicit formulas for these generating series in terms of monomial symmetric functions by introducing a bijection between partitioned hypermaps on (locally) orientable surfaces and some decorated forests and trees. Thanks to purely algebraic means, we recover the formula for the class algebra and provide a new simpler formula for the double coset algebra. As a salient ingredient, we compute an explicit formulation for zonal polynomials indexed by partitions of type [a, b, 1 n−a−b]. Résumé. Cet article est dédié au calcul explicite des séries génératrices des constantes de structure de deux sousalgèbres commutatives de l’algèbre de groupe du groupe symétrique, l’algèbre de classes et l’algèbre de double classe latérale. Tel que montré par Hanlon, Stanley and Stembridge (1992), ces séries déterminent la distribution spectrale de certaines matrices aléatoires importantes en statistique. Morales et Vassilieva (2009, 2011) ont trouvé des formules explicites pour ces séries génératrices en termes des monômes symétriques en introduisant une bijection entre les hypercartes partitionées sur des surfaces (localement) orientables et certains arbres et forêts décorées. Grâce à des moyens purement algébriques, nous retrouvons la formule pour l’algèbre de classe et déterminons une nouvelle formule plus simple pour l’algèbre de double classe latérale. En tant que point saillant de notre démonstration nous calculons une formulation explicite pour les polynômes zonaux indexés par des partitions de type [a, b, 1 n−a−b].
THE BERNARDI PROCESS AND TORSOR STRUCTURES ON SPANNING TREES
"... Abstract. Let G be a ribbon graph, i.e., a connected finite graph G together with a cyclic ordering of the edges around each vertex. By adapting a construction due to Olivier Bernardi, we associate to any pair (v, e) consisting of a vertex v and an edge e adjacent to v a bijection β(v,e) between spa ..."
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Abstract. Let G be a ribbon graph, i.e., a connected finite graph G together with a cyclic ordering of the edges around each vertex. By adapting a construction due to Olivier Bernardi, we associate to any pair (v, e) consisting of a vertex v and an edge e adjacent to v a bijection β(v,e) between
Mahler's Measure and Special Values of Lfunctions
, 1998
"... this paper is to describe an attempt to understand and generalize a recent formula of Deninger [1997] by means of systematic numerical experiment. This conjectural formula, ..."
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Cited by 79 (1 self)
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this paper is to describe an attempt to understand and generalize a recent formula of Deninger [1997] by means of systematic numerical experiment. This conjectural formula,
Scaling limit of random planar maps Lecture 1.
, 2008
"... A planar map is a connected planar graph embedded in the sphere and considered up to deformation. = = ..."
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A planar map is a connected planar graph embedded in the sphere and considered up to deformation. = =
Automorphic forms and Lorentzian KacMoody algebras
 Part II,, Preprint RIMS 1122, Kyoto
, 1996
"... Abstract. Using the general method which was applied to prove finiteness of the set of hyperbolic generalized Cartan matrices of elliptic and parabolic type, we classify all symmetric (and twisted to symmetric) hyperbolic generalized Cartan matrices of elliptic type and of rank 3 with a lattice Weyl ..."
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Cited by 62 (25 self)
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Abstract. Using the general method which was applied to prove finiteness of the set of hyperbolic generalized Cartan matrices of elliptic and parabolic type, we classify all symmetric (and twisted to symmetric) hyperbolic generalized Cartan matrices of elliptic type and of rank 3 with a lattice Weyl vector. We develop the general theory of reflective lattices T with 2 negative squares and reflective automorphic forms on homogeneous domains of type IV defined by T. We consider this theory as mirror symmetric to the theory of elliptic and parabolic hyperbolic reflection groups and corresponding hyperbolic root systems. We formulate Arithmetic Mirror Symmetry Conjecture relating both these theories and prove some statements to support this Conjecture. This subject is connected with automorphic correction of Lorentzian Kac–Moody algebras. We define Lie reflective automorphic forms which are the most beautiful automorphic forms defining automorphic Lorentzian Kac–Moody algebras and formulate finiteness Conjecture for these forms. Detailed study of automorphic correction and Lie reflective automorphic forms for generalized Cartan matrices mentioned above will be given in Part II. 0.
New data on European Astragalusfeeding Bruchidius, with the description of a new species from Southern Italy
"... ABSTRACT. Bruchidius bernardi n. sp., a seedbeetle feeding in Astragalus depressus pods, is described from southern Italy. A new synonymy is proposed: Bruchidius myobromae (MOTSCHULSKY, 1874) ( = Mylabris virgata var. scutulata BAUDI, 1890). The host plant of Bruchidius poecilus (GERMAR) in the sam ..."
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ABSTRACT. Bruchidius bernardi n. sp., a seedbeetle feeding in Astragalus depressus pods, is described from southern Italy. A new synonymy is proposed: Bruchidius myobromae (MOTSCHULSKY, 1874) ( = Mylabris virgata var. scutulata BAUDI, 1890). The host plant of Bruchidius poecilus (GERMAR
Algebraizations Of Quantifier Logics, An Introductory Overview
, 1991
"... . This work is an introduction: in particular, to algebras of relations of various ranks, and in general, to the part of algebraic logic algebraizing quantifier logics as well as those propositional logics (like modal logics) in the semantics of which theories of relations play an essential role. ..."
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. This work is an introduction: in particular, to algebras of relations of various ranks, and in general, to the part of algebraic logic algebraizing quantifier logics as well as those propositional logics (like modal logics) in the semantics of which theories of relations play an essential role. This work has a survey character, too. The most frequently used algebras like cylindric, relation, polyadic, and quasipolyadic algebras are carefully introduced and intuitively explained for the nonspecialist. Their variants, connections with logic, abstract model theory, and further algebraic logics are also reviewed. Efforts were made to make the review part relatively comprehensive. In some directions we tried to give an overview of the most recent results and research trends, too. Contents 1. Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2. Gett...
A site and timeheterogeneous model of aminoacid replacement
, 2007
"... 1 We combined the CAT mixture model (Lartillot and Philippe 2004) and the nonstationary BP model (Blanquart and Lartillot 2006) into a new model, CATBP, accounting for variations of the evolutionary process both along the sequence and across lineages. As in CAT, the model implements a mixture of d ..."
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Cited by 42 (6 self)
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1 We combined the CAT mixture model (Lartillot and Philippe 2004) and the nonstationary BP model (Blanquart and Lartillot 2006) into a new model, CATBP, accounting for variations of the evolutionary process both along the sequence and across lineages. As in CAT, the model implements a mixture of distinct Markovian processes of substitution distributed among sites, thus accommodating sitespecific selective constraints induced by protein structure and function. Furthermore, as in BP, these processes are nonstationary, and their equilibrium frequencies are allowed to change along lineages in a correlated way, through discrete shifts in global amino acid composition distributed along the phylogenetic tree. We implemented the CATBP model in a Bayesian Markov Chain Monte Carlo framework, and compared its predictions with those of three simpler models, BP, CAT, and the site and timehomogeneous GTR model, on a concatenation of four mitochondrial proteins of 20 arthropod species. In contrast to GTR, BP and CAT, which all display a phylogenetic reconstruction artefact positioning the bees Apis m. and Melipona b. among chelicerates, the CATBP model
2D/3D TURBINE SIMULATIONS WITH FREEFEM
"... Abstract. The purpose of this document is to illustrate how a new generation of open source “General Purpose ” Finite Element Solvers make it possible to solve complex, two or threedimensional problems. Olivier Pironneau initiated this tendancy by proposing, in the 80’s, its pioneering freefem so ..."
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Abstract. The purpose of this document is to illustrate how a new generation of open source “General Purpose ” Finite Element Solvers make it possible to solve complex, two or threedimensional problems. Olivier Pironneau initiated this tendancy by proposing, in the 80’s, its pioneering freefem
Results 1  10
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812