2016, Graduate studies in mathematics, ISBN 9780821848418, Volume 172, xi, 461

Random matrices (probabilistic aspects; for algebraic aspects see 15B52) | Equations of mathematical physics and other areas of application | Partial differential equations | Approximations and expansions | Probability theory and stochastic processes | Special matrices | Operator theory | Probability theory on algebraic and topological structures | Riemann-Hilbert problems | Exact enumeration problems, generating functions | Convex and discrete geometry | Special classes of linear operators | Combinatorics | Asymptotic approximations, asymptotic expansions (steepest descent, etc.) | Time-dependent statistical mechanics (dynamic and nonequilibrium) | Enumerative combinatorics | Exactly solvable dynamic models | Linear and multilinear algebra; matrix theory | Special processes | Statistical mechanics, structure of matter | Toeplitz operators, Hankel operators, Wiener-Hopf operators | Tilings in $2$ dimensions | Interacting random processes; statistical mechanics type models; percolation theory | Discrete geometry | Random matrices | Combinatorial analysis

Book

2016, ISBN 9781470427245, xiv, 352 pages

Book

Acta Arithmetica, ISSN 0065-1036, 2017, Volume 181, Issue 1, pp. 27 - 55

... (Digital functions and distribution of binomial coefficients, J. London Math. Soc. (2) 64(3), 2001), that $\vartheta_p(j,n)/\vartheta_p(0,n)$ is given by a polynomial...

MATHEMATICS | NUMBER | generating functions | FIXED POWER | DIGITAL SUMS | CONGRUENCE | binomial coefficients modulo powers of primes | exact enumeration | DIVIDES | PASCAL TRIANGLE

MATHEMATICS | NUMBER | generating functions | FIXED POWER | DIGITAL SUMS | CONGRUENCE | binomial coefficients modulo powers of primes | exact enumeration | DIVIDES | PASCAL TRIANGLE

Journal Article

1984, ISBN 9780821845127, Volume 59., x, 286

Book

Theoretical Computer Science, ISSN 0304-3975, 09/2013, Volume 502, pp. 4 - 15

...? I solved this problem for doughnuts with up to 10 holes, and my colleagues Alain Giorgetti and Alexander Mednykh counted maps by number of edges alone on doughnuts with up to 11 holes...

Orientable surfaces | Exact enumeration | Rooted maps | Orbifolds | Unrooted maps | Generating functions | NUMBER | PLANAR MAPS | GENUS | ENUMERATION | COMPUTER SCIENCE, THEORY & METHODS | ORIENTABLE SURFACE

Orientable surfaces | Exact enumeration | Rooted maps | Orbifolds | Unrooted maps | Generating functions | NUMBER | PLANAR MAPS | GENUS | ENUMERATION | COMPUTER SCIENCE, THEORY & METHODS | ORIENTABLE SURFACE

Journal Article

Mathematical programming, ISSN 0025-5610, 2001, Volume 90, Issue 2, pp. 273 - 290

We present a polynomial time algorithm to find the maximum weight of an edge-cut in graphs embeddable on an arbitrary orientable surface, with integral weights...

cut – generating function – Pfaffian orientation – modular arithmetics | Modular arithmetics | Cut | Generating function | Pfaffian orientation | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MAXIMUM CUT | EIGENVALUES | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | cut | NESTED DISSECTION | generating function | EXACT GROUND-STATES | modular arithmetics | ISING SPIN-GLASSES

cut – generating function – Pfaffian orientation – modular arithmetics | Modular arithmetics | Cut | Generating function | Pfaffian orientation | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MAXIMUM CUT | EIGENVALUES | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | cut | NESTED DISSECTION | generating function | EXACT GROUND-STATES | modular arithmetics | ISING SPIN-GLASSES

Journal Article

Communications in statistics. Theory and methods, ISSN 0361-0926, 06/2020, pp. 1 - 13

... patterns, while itself an interesting mathematical problem, has found many applications in various fields (Balakrishnan and Koutras 2002; Fu and Lou 2003...

Journal Article

Quarterly Journal of the Belgian, French and Italian Operations Research Societies, ISSN 1619-4500, 3/2003, Volume 1, Issue 1, pp. 67 - 83

... of fast enumeration algorithms. This paper considers the isomeric acyclic structures focusing on the enumeration of the alkane molecular family...

Economics | generating functions | Exact enumeration problems | trees | enumeration of graphs and maps | applications | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Combinatorial enumeration problems | Algorithms | Research | Methods | Studies

Economics | generating functions | Exact enumeration problems | trees | enumeration of graphs and maps | applications | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Combinatorial enumeration problems | Algorithms | Research | Methods | Studies

Journal Article

Journal of Difference Equations and Applications, ISSN 1023-6198, 05/2011, Volume 17, Issue 5, pp. 709 - 720

We apply ideas from the cluster method to q-count the permutations of a multiset according to the number of occurrences of certain generalized patterns, as...

generating functions | permutation patterns | q-difference equations | exact enumeration | Permutation patterns | Exact enumeration | Generating functions | MATHEMATICS, APPLIED | Clusters | Permutations | Collection | Difference equations | Statistics | Counting

generating functions | permutation patterns | q-difference equations | exact enumeration | Permutation patterns | Exact enumeration | Generating functions | MATHEMATICS, APPLIED | Clusters | Permutations | Collection | Difference equations | Statistics | Counting

Journal Article

Combinatorics, probability & computing, ISSN 0963-5483, 01/2015, Volume 24, Issue 1, pp. 1 - 53

We study the coefficients of algebraic functions ∑ n≥0 f n z n . First, we recall the too-little-known fact that these coefficients f n always admit a closed form...

Paper | UNIFORM RANDOM GENERATION | ANALYTIC COMBINATORICS | ENUMERATION | STATISTICS & PROBABILITY | LANGUAGES | DISTRIBUTIONS | MATHEMATICS | SINGULARITY ANALYSIS | POWER-SERIES | CONTEXT-FREE PAIRS | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS | PROBABILITIES | Theorems | Algebra | Algorithms | Asymptotic properties | Mathematical analysis | Exact solutions | Mathematical models | Grammars

Paper | UNIFORM RANDOM GENERATION | ANALYTIC COMBINATORICS | ENUMERATION | STATISTICS & PROBABILITY | LANGUAGES | DISTRIBUTIONS | MATHEMATICS | SINGULARITY ANALYSIS | POWER-SERIES | CONTEXT-FREE PAIRS | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS | PROBABILITIES | Theorems | Algebra | Algorithms | Asymptotic properties | Mathematical analysis | Exact solutions | Mathematical models | Grammars

Journal Article

Annals of Combinatorics, ISSN 0218-0006, 12/2016, Volume 20, Issue 4, pp. 661 - 704

.... The classification is now complete for walks with steps in $${\{0, \pm 1\}^{2}}$$ { 0 , ± 1 } 2 : the generating function is D-finite if and only if a certain group associated with the step set is finite...

Mathematics | D-finite series | Combinatorics | 05A15 | exact enumeration | lattice walks | MATHEMATICS, APPLIED | FACTORIZATION | SERIES | D-FINITE | DIFFERENTIAL-OPERATORS | Algebra

Mathematics | D-finite series | Combinatorics | 05A15 | exact enumeration | lattice walks | MATHEMATICS, APPLIED | FACTORIZATION | SERIES | D-FINITE | DIFFERENTIAL-OPERATORS | Algebra

Journal Article

12.
Full Text
A Simple Recurrence for Covers of the Sphere With Branch Points of Arbitrary Ramification

Annals of Combinatorics, ISSN 0218-0006, 12/2006, Volume 10, Issue 4, pp. 431 - 441

The problem of counting ramified covers of a Riemann surface up to homeomorphism was proposed by Hurwitz in the late 1800...

minimal | m -Eulerian trees | generating functions | Mathematics | Combinatorics | ramified covers | 05A15 | 58D29 | permutation factorizations | exact enumeration | transitive | 14H10 | Permutation factorizations | Generating functions | Transitive | Exact enumeration | m-Eulerian trees | Ramified covers | Minimal | MATHEMATICS, APPLIED

minimal | m -Eulerian trees | generating functions | Mathematics | Combinatorics | ramified covers | 05A15 | 58D29 | permutation factorizations | exact enumeration | transitive | 14H10 | Permutation factorizations | Generating functions | Transitive | Exact enumeration | m-Eulerian trees | Ramified covers | Minimal | MATHEMATICS, APPLIED

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 2/2001, Volume 102, Issue 3, pp. 865 - 881

...), for the growth constant of trees, and confirms to a very high degree of certainty that both the animal and tree generating functions have a logarithmic divergence...

lattice animals | computer algorithms | Physical Chemistry | Mathematical and Computational Physics | Quantum Physics | exact enumeration | Physics | Statistical Physics | Computer algorithms | Exact enumeration | Lattice animals | SERIES | STATISTICS | PERCOLATION | POLYOMINOES | ATTACK | PHYSICS, MATHEMATICAL | Physics - Statistical Mechanics

lattice animals | computer algorithms | Physical Chemistry | Mathematical and Computational Physics | Quantum Physics | exact enumeration | Physics | Statistical Physics | Computer algorithms | Exact enumeration | Lattice animals | SERIES | STATISTICS | PERCOLATION | POLYOMINOES | ATTACK | PHYSICS, MATHEMATICAL | Physics - Statistical Mechanics

Journal Article

Discrete Mathematics, ISSN 0012-365X, 04/2014, Volume 321, Issue 1, pp. 12 - 23

.... We also compute the generating function of Dyck paths avoiding any single pattern in a recursive fashion, from which we deduce the exact enumeration of such a class of paths. Finally, we describe the asymptotic behavior of the sequence counting Dyck paths avoiding a generic pattern, we prove that the Dyck pattern poset is a well-ordering and we propose a list of open problems.

Poset | Pattern | Exact enumeration | Dyck path | Asymptotic | MATHEMATICS | AVOIDANCE | SET PARTITIONS | Polypropylenes | Asymptotic properties | Mathematical analysis | Covering | Set theory | Mathematical models | Recursive | Counting | Combinatorics | Mathematics

Poset | Pattern | Exact enumeration | Dyck path | Asymptotic | MATHEMATICS | AVOIDANCE | SET PARTITIONS | Polypropylenes | Asymptotic properties | Mathematical analysis | Covering | Set theory | Mathematical models | Recursive | Counting | Combinatorics | Mathematics

Journal Article

ACM Transactions on Algorithms (TALG), ISSN 1549-6325, 10/2009, Volume 5, Issue 4, pp. 1 - 27

We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP...

Exponential-time algorithm | discrete optimization | generating function | exact algorithm | constraint satisfaction | partition function | Constraint satisfaction | Discrete optimization | Partition function | Generating function | Exact algorithm | MATHEMATICS, APPLIED | PATHWIDTH | BOUNDS | COMPLEXITY | COMPUTER SCIENCE, THEORY & METHODS | ALGORITHMS | Partitions | Algorithms | Mathematical analysis | Graphs | Ising model | Mathematical models | Optimization

Exponential-time algorithm | discrete optimization | generating function | exact algorithm | constraint satisfaction | partition function | Constraint satisfaction | Discrete optimization | Partition function | Generating function | Exact algorithm | MATHEMATICS, APPLIED | PATHWIDTH | BOUNDS | COMPLEXITY | COMPUTER SCIENCE, THEORY & METHODS | ALGORITHMS | Partitions | Algorithms | Mathematical analysis | Graphs | Ising model | Mathematical models | Optimization

Journal Article

Ergodic theory and dynamical systems, ISSN 0143-3857, 06/2015, Volume 35, Issue 4, pp. 1315 - 1344

The enumeration of combinatorial classes of the complex polynomial vector fields in $ \mathbb{C} $ presented by K. Dias...

MATHEMATICS | MATHEMATICS, APPLIED | Topological manifolds | Dynamical systems | Polynomials | Enumeration | Unity | Mathematical analysis | Exact solutions | Tools | Fields (mathematics) | Combinatorial analysis

MATHEMATICS | MATHEMATICS, APPLIED | Topological manifolds | Dynamical systems | Polynomials | Enumeration | Unity | Mathematical analysis | Exact solutions | Tools | Fields (mathematics) | Combinatorial analysis

Journal Article

Nuclear Physics, Section B, ISSN 0550-3213, 1999, Volume 556, Issue 3, pp. 445 - 462

We examine the Ising chain in a transverse field at zero temperature from the point of view of a family of moment formalisms based upon the cumulant generating function, where we find exact solutions...

Exact enumeration problems | Quantum equilibrium statistical mechanics | Interacting particle systems | Asymptotic representations in the complex domain | Exactly solvable models | Moment problems | Critical phenomena | Lattice systems | Characteristic functions | Phase transitions | LATTICE GAUGE-THEORY | asymptotic representations in the complex domain | interacting particle systems | critical phenomena | moment problems | exact enumeration problems | phase transitions | PHYSICS, NUCLEAR | exactly solvable models | lattice systems | SYSTEMS | T-EXPANSION | quantum equilibrium statistical mechanics | characteristic functions | TOOL | PHYSICS, PARTICLES & FIELDS

Exact enumeration problems | Quantum equilibrium statistical mechanics | Interacting particle systems | Asymptotic representations in the complex domain | Exactly solvable models | Moment problems | Critical phenomena | Lattice systems | Characteristic functions | Phase transitions | LATTICE GAUGE-THEORY | asymptotic representations in the complex domain | interacting particle systems | critical phenomena | moment problems | exact enumeration problems | phase transitions | PHYSICS, NUCLEAR | exactly solvable models | lattice systems | SYSTEMS | T-EXPANSION | quantum equilibrium statistical mechanics | characteristic functions | TOOL | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, 12/2012, Volume 2012, Issue 12, pp. 1 - 13

Enumeration of molecules is one of the fundamental problems in bioinformatics and plays an important role in drug discovery, experimental structure elucidation (e.g...

computational biology | exact results | bioinformatics | WIENER INDEXES | NUMBER | BENZENE | POLYMERIZATION | PHYSICS, MATHEMATICAL | MOLECULES | MECHANICS | SYSTEMS | P-POLYPHENYL | CHAINS | POLYCHLORINATED-BIPHENYLS | Polyphenyls | Enumeration | Asymptotic properties | Mathematical analysis | Mathematical models | Recursion | Bioinformatics | Isomers

computational biology | exact results | bioinformatics | WIENER INDEXES | NUMBER | BENZENE | POLYMERIZATION | PHYSICS, MATHEMATICAL | MOLECULES | MECHANICS | SYSTEMS | P-POLYPHENYL | CHAINS | POLYCHLORINATED-BIPHENYLS | Polyphenyls | Enumeration | Asymptotic properties | Mathematical analysis | Mathematical models | Recursion | Bioinformatics | Isomers

Journal Article

Advances in mathematical physics, ISSN 1687-9120, 7/2017, Volume 2017, pp. 1 - 5

The partition function for the random walk of an electrostatic field produced by several static parallel infinite charged planes in which the charge distribution could be either ±σ is obtained...

DIMENSIONAL SYSTEM | EXACT STATISTICAL-MECHANICS | ENUMERATION | DYCK PATHS | PHYSICS, MATHEMATICAL | COULOMB FORCES | Numerical analysis | Random variables | Lightning | Static electricity

DIMENSIONAL SYSTEM | EXACT STATISTICAL-MECHANICS | ENUMERATION | DYCK PATHS | PHYSICS, MATHEMATICAL | COULOMB FORCES | Numerical analysis | Random variables | Lightning | Static electricity

Journal Article

Proteins: Structure, Function, and Bioinformatics, ISSN 0887-3585, 06/2015, Volume 83, Issue 6, pp. 1054 - 1067

.... In this work, we develop a method for protein rigid domain identification based on an exhaustive enumeration of maximal rigid domains, the rigid domains not fully contained within other domains...

protein structure | hinge | normal mode analysis | graph theory | elastic network model | exhaustive enumeration | DAGR | exact | maximal clique | rigid domain | Hinge | Maximal clique | Elastic network model | Normal mode analysis | Graph theory | Rigid domain | Exact | Protein structure | Exhaustive enumeration | MOLECULAR-DYNAMICS | FLUCTUATION DYNAMICS | SINGLE-PARAMETER | FREQUENCY NORMAL-MODES | BIOCHEMISTRY & MOLECULAR BIOLOGY | FLEXIBILITY | ELASTIC NETWORK MODELS | MOTIONS | CONFORMATIONAL-CHANGE | BIOPHYSICS | LIGAND DOCKING | NORMAL-MODE ANALYSIS | Protein Structure, Tertiary | Sequence Analysis, Protein - methods | Computational Biology - methods | Algorithms | Software | Proteins - chemistry | Molecular Dynamics Simulation | Proteins | Analysis | Methods

protein structure | hinge | normal mode analysis | graph theory | elastic network model | exhaustive enumeration | DAGR | exact | maximal clique | rigid domain | Hinge | Maximal clique | Elastic network model | Normal mode analysis | Graph theory | Rigid domain | Exact | Protein structure | Exhaustive enumeration | MOLECULAR-DYNAMICS | FLUCTUATION DYNAMICS | SINGLE-PARAMETER | FREQUENCY NORMAL-MODES | BIOCHEMISTRY & MOLECULAR BIOLOGY | FLEXIBILITY | ELASTIC NETWORK MODELS | MOTIONS | CONFORMATIONAL-CHANGE | BIOPHYSICS | LIGAND DOCKING | NORMAL-MODE ANALYSIS | Protein Structure, Tertiary | Sequence Analysis, Protein - methods | Computational Biology - methods | Algorithms | Software | Proteins - chemistry | Molecular Dynamics Simulation | Proteins | Analysis | Methods

Journal Article

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