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Clausal Discovery
 Machine Learning
, 1996
"... The clausal discovery engine Claudien is presented. Claudien is an inductive logic programming engine that fits in the knowledge discovery in databases and data mining paradigm as it discovers regularities that are valid in data. As such Claudien performs a novel induction task, which is called char ..."
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Cited by 184 (33 self)
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The clausal discovery engine Claudien is presented. Claudien is an inductive logic programming engine that fits in the knowledge discovery in databases and data mining paradigm as it discovers regularities that are valid in data. As such Claudien performs a novel induction task, which is called characteristic induction from closed observations, and which is related to existing formalizations of induction in logic. In characterising induction from closed observations, the regularities are represented by clausal theories, and the data using Herbrand interpretations. Claudien also employs a novel declarative bias mechanism to define the set of clauses that may appear in a hypothesis. Keywords : Inductive Logic Programming, Knowledge Discovery in Databases, Data Mining, Learning, Induction, Semantics for Induction, Logic of Induction, Parallel Learning. 1 Introduction Despite the fact that the areas of knowledge discovery in databases [Fayyad et al., 1995] and inductive logic programmin...
SeibergWitten prepotential from instanton counting,” hepth/0206161
"... In my lecture I consider integrals over moduli spaces of supersymmetric gauge field configurations (instantons, Higgs bundles, torsion free sheaves). The applications are twofold: physical and mathematical; they involve supersymmetric quantum mechanics of Dparticles in various dimensions, direct co ..."
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Cited by 148 (5 self)
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In my lecture I consider integrals over moduli spaces of supersymmetric gauge field configurations (instantons, Higgs bundles, torsion free sheaves). The applications are twofold: physical and mathematical; they involve supersymmetric quantum mechanics of Dparticles in various dimensions, direct computation of the celebrated SeibergWitten prepotential, sum rules for the solutions of the Bethe ansatz equations and their relation to the Laumon’s nilpotent cone. As a byproduct we derive some combinatoric identities involving the sums over Young tableaux. 1.
Longest increasing subsequences: from patience sorting to the BaikDeiftJohansson theorem
 Bull. Amer. Math. Soc. (N.S
, 1999
"... Abstract. We describe a simple oneperson card game, patience sorting. Its analysis leads to a broad circle of ideas linking Young tableaux with the longest increasing subsequence of a random permutation via the Schensted correspondence. A recent highlight of this area is the work of BaikDeiftJoha ..."
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Cited by 136 (2 self)
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Abstract. We describe a simple oneperson card game, patience sorting. Its analysis leads to a broad circle of ideas linking Young tableaux with the longest increasing subsequence of a random permutation via the Schensted correspondence. A recent highlight of this area is the work of BaikDeiftJohansson which yields limiting probability laws via hard analysis of Toeplitz determinants. 1.
Asymptotics of Plancherel measures for symmetric groups
 J. Amer. Math. Soc
, 2000
"... 1.1. Plancherel measures. Given a finite group G, by the corresponding Plancherel measure we mean the probability measure on the set G ∧ of irreducible representations of G which assigns to a representation π ∈ G ∧ the weight (dim π) 2 /G. For the symmetric group S(n), the set S(n) ∧ is the set o ..."
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Cited by 136 (33 self)
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1.1. Plancherel measures. Given a finite group G, by the corresponding Plancherel measure we mean the probability measure on the set G ∧ of irreducible representations of G which assigns to a representation π ∈ G ∧ the weight (dim π) 2 /G. For the symmetric group S(n), the set S(n) ∧ is the set of partitions λ of the number
Some Combinatorial Properties of Schubert Polynomials
, 1993
"... Schubert polynomials were introduced by Bernstein Gelfand Gelfand and De mazure, and were extensively developed by Lascoux, Schiitzenberger, Macdonald, and others. We give an explicit combinatorial interpretation of the Schubert polyno mial in terms of the reduced decompositions of the permutation ..."
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Cited by 123 (10 self)
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Schubert polynomials were introduced by Bernstein Gelfand Gelfand and De mazure, and were extensively developed by Lascoux, Schiitzenberger, Macdonald, and others. We give an explicit combinatorial interpretation of the Schubert polyno mial in terms of the reduced decompositions of the permutation w. Using this Supported by the National Physical Science Consortium.
Conjectures on the quotient ring by diagonal invariants
 J. ALGEBRAIC COMBIN
, 1994
"... We formulate a series of conjectures (and a few theorems) on the quotient of the polynomial ring Q[x1,...,xn,y1,...,yn] in two sets of variables by the ideal generated by all Sn invariant polynomials without constant term. The theory of the corresponding ring in a single set of variables X = {x1,.. ..."
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Cited by 98 (10 self)
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We formulate a series of conjectures (and a few theorems) on the quotient of the polynomial ring Q[x1,...,xn,y1,...,yn] in two sets of variables by the ideal generated by all Sn invariant polynomials without constant term. The theory of the corresponding ring in a single set of variables X = {x1,...,xn} is classical. Introducing the second set of variables leads to a ring about which little is yet understood, but for which there is strong evidence of deep connections with many fundamental results of enumerative combinatorics, as well as with algebraic geometry and Lie theory.
Matrix models for betaensembles
 J. Math. Phys
, 2002
"... This paper constructs tridiagonal random matrix models for general (β> 0) βHermite (Gaussian) and βLaguerre (Wishart) ensembles. These generalize the wellknown Gaussian and Wishart models for β = 1,2,4. Furthermore, in the cases of the βLaguerre ensembles, we eliminate the exponent quantization ..."
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Cited by 86 (19 self)
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This paper constructs tridiagonal random matrix models for general (β> 0) βHermite (Gaussian) and βLaguerre (Wishart) ensembles. These generalize the wellknown Gaussian and Wishart models for β = 1,2,4. Furthermore, in the cases of the βLaguerre ensembles, we eliminate the exponent quantization present in the previously known models. We further discuss applications for the new matrix models, and present some open problems.
ALGEBRAIC ASPECTS OF INCREASING SUBSEQUENCES
 DUKE MATHEMATICAL JOURNAL VOL. 109, NO. 1
, 2001
"... We present a number of results relating partial CauchyLittlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae for the distribution of the longest increasing subsequence of a random involution with constrained number ..."
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Cited by 71 (10 self)
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We present a number of results relating partial CauchyLittlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae for the distribution of the longest increasing subsequence of a random involution with constrained number of fixed points; new formulae for partial CauchyLittlewood sums, as well as new proofs of old formulae; relations of these expressions to orthogonal polynomials on the unit circle; and explicit bases for invariant spaces of the classical groups, together with appropriate generalizations of the straightening algorithm.
A New Class Of Symmetric Functions
 Publ. I.R.M.A. Strasbourg, 372/S20, Actes 20 S'eminaire Lotharingien
, 1988
"... Contents. 1. Introduction 2. The symmetric functions P (q; t) 3. Duality 4. Skew P and Q functions 5. Explicit formulas 6. The Kostka matrix 7. Another scalar product 8. Conclusion 9. Appendix 1. Introduction I will begin by reviewing briefly some aspects of the theory of symmetric functions. Thi ..."
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Cited by 70 (1 self)
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Contents. 1. Introduction 2. The symmetric functions P (q; t) 3. Duality 4. Skew P and Q functions 5. Explicit formulas 6. The Kostka matrix 7. Another scalar product 8. Conclusion 9. Appendix 1. Introduction I will begin by reviewing briefly some aspects of the theory of symmetric functions. This will serve to fix notation and to provide some motivation for the subject of these lectures. Let x 1 , : : : , xn be independent indeterminates. The symmetric group Sn acts on the polynomial ring Z[x 1 ; : : : ; xn ] by permuting the x's, and we shall write n = Z[x 1 ; : : : ; xn ] Sn for the subring of symmetric polynomials in x<F8