Experimental Mathematics, ISSN 1058-6458, 01/2006, Volume 15, Issue 2, pp. 187 - 191

We present a case study in experimental yet rigorous mathematics by describing an algorithm, fully implemented in both Mathematica and Maple, that...

Dyson's conjecture | 05-04 | constant term | Dyson’s conjecture | Constant term | MATHEMATICS | STATISTICAL THEORY | PROOF | ENERGY LEVELS | Mathematics - Combinatorics

Dyson's conjecture | 05-04 | constant term | Dyson’s conjecture | Constant term | MATHEMATICS | STATISTICAL THEORY | PROOF | ENERGY LEVELS | Mathematics - Combinatorics

Journal Article

Experimental Mathematics, ISSN 1058-6458, 04/2019, Volume 28, Issue 2, pp. 194 - 208

For integers k, n, c with k, n ⩾ 1, and c ⩾ 0, the n-color weak Rado number is defined as the least integer N, if it exists, such that for every n-coloring of...

weakly sum-free sets | weak Rado numbers | 05-04 | 05C55 | 05D10 | sum-free sets | weak Schur numbers | Schur numbers | Rado numbers | 05A17 | MATHEMATICS

weakly sum-free sets | weak Rado numbers | 05-04 | 05C55 | 05D10 | sum-free sets | weak Schur numbers | Schur numbers | Rado numbers | 05A17 | MATHEMATICS

Journal Article

Annals of Mathematics and Artificial Intelligence, ISSN 1012-2443, 12/2017, Volume 81, Issue 3, pp. 315 - 327

Discovery in mathematics is a prototypical intelligent behavior, and an early and continuing goal of artificial intelligence research. We present a heuristic...

05-04 | 05C45 | Automated mathematical discovery | Automated conjecturing | Complex Systems | Computer Science | Artificial Intelligence (incl. Robotics) | Mathematics, general | Property-relations conjectures | Computer Science, general | 05C69 | Computer science

05-04 | 05C45 | Automated mathematical discovery | Automated conjecturing | Complex Systems | Computer Science | Artificial Intelligence (incl. Robotics) | Mathematics, general | Property-relations conjectures | Computer Science, general | 05C69 | Computer science

Journal Article

Advances in Computational Mathematics, ISSN 1019-7168, 4/2019, Volume 45, Issue 2, pp. 519 - 561

In this paper, a deterministic sparse Fourier transform algorithm is presented which breaks the quadratic-in-sparsity runtime bottleneck for a large class of...

Sparse Fourier transform (SFT) | Visualization | Computational Mathematics and Numerical Analysis | Structured sparsity | 65T50 | 65T40 | Mathematical and Computational Biology | Mathematics | 68W25 | Computational Science and Engineering | Deterministic constructions | 05-04 | 42A15 | 42A10 | 42A32 | Approximation algorithms | Mathematical Modeling and Industrial Mathematics | 42A16 | 94A12 | MATHEMATICS, APPLIED | Fourier transformations | Algorithms | Research | Periodic functions | Mathematical research

Sparse Fourier transform (SFT) | Visualization | Computational Mathematics and Numerical Analysis | Structured sparsity | 65T50 | 65T40 | Mathematical and Computational Biology | Mathematics | 68W25 | Computational Science and Engineering | Deterministic constructions | 05-04 | 42A15 | 42A10 | 42A32 | Approximation algorithms | Mathematical Modeling and Industrial Mathematics | 42A16 | 94A12 | MATHEMATICS, APPLIED | Fourier transformations | Algorithms | Research | Periodic functions | Mathematical research

Journal Article

Designs, Codes and Cryptography, ISSN 0925-1022, 4/2019, Volume 87, Issue 4, pp. 931 - 953

In the 1960s, Hirschfeld embarked on a program to classify cubic surfaces with 27 lines over finite fields. This work is a contribution to this problem. We...

Information and Communication, Circuits | Finite field | 68R05 | Cryptology | Double-six | 14J10 | 51E25 | Data Structures and Information Theory | Geometry | 05-04 | Discrete Mathematics in Computer Science | Computer Science | Classification | Coding and Information Theory | Cubic surface | 05B25 | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | Algorithms

Information and Communication, Circuits | Finite field | 68R05 | Cryptology | Double-six | 14J10 | 51E25 | Data Structures and Information Theory | Geometry | 05-04 | Discrete Mathematics in Computer Science | Computer Science | Classification | Coding and Information Theory | Cubic surface | 05B25 | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | Algorithms

Journal Article

Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 04/2015, Volume 131, pp. 32 - 60

Solutions to a linear Diophantine system, or lattice points in a rational convex polytope, are important concepts in algebraic combinatorics and computational...

Polytopes | MacMahon's partition analysis | Lattice points | Ehrhart polynomials | MATHEMATICS | POLYHEDRA | POINTS | Algorithms | Mathematics - Combinatorics

Polytopes | MacMahon's partition analysis | Lattice points | Ehrhart polynomials | MATHEMATICS | POLYHEDRA | POINTS | Algorithms | Mathematics - Combinatorics

Journal Article

Foundations of Computational Mathematics, ISSN 1615-3375, 6/2010, Volume 10, Issue 3, pp. 303 - 338

We study the problem of estimating the best k term Fourier representation for a given frequency sparse signal (i.e., vector) A of length N≫k. More explicitly,...

65T50 | Economics general | 65T40 | Trigonometric approximation and interpolation | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Discrete and fast Fourier transforms | 68W25 | 05-04 | 42A15 | Numerical Analysis | 42A10 | 42A32 | Approximation algorithms | Math Applications in Computer Science | Applications of Mathematics | Computer Science, general | 94A12 | MATHEMATICS | MATHEMATICS, APPLIED | ORTHOGONAL MATCHING PURSUIT | SIGNAL RECOVERY | TRANSFORM | COMPUTER SCIENCE, THEORY & METHODS | COMPUTATION

65T50 | Economics general | 65T40 | Trigonometric approximation and interpolation | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Discrete and fast Fourier transforms | 68W25 | 05-04 | 42A15 | Numerical Analysis | 42A10 | 42A32 | Approximation algorithms | Math Applications in Computer Science | Applications of Mathematics | Computer Science, general | 94A12 | MATHEMATICS | MATHEMATICS, APPLIED | ORTHOGONAL MATCHING PURSUIT | SIGNAL RECOVERY | TRANSFORM | COMPUTER SCIENCE, THEORY & METHODS | COMPUTATION

Journal Article

LMS Journal of Computation and Mathematics, ISSN 1461-1570, 2014, Volume 17, Issue 1, pp. 24 - 32

We show that if a Barker sequence of length n > 13 exists, then either n = 3979201339721749133016171583224100, or n > 4.10(33). This improves the lower bound...

MATHEMATICS | MATHEMATICS, APPLIED

MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Experimental Mathematics, ISSN 1058-6458, 06/2011, Volume 20, Issue 2, pp. 145 - 152

We investigate experimentally the growth regimes of the number of LEGO structures that can be constructed contiguously from n blocks of equal shape and color.

05-04 | LEGO | Monte Carlo methods | 05A16 | asymptotic enumeration | Asymptotic enumeration | MATHEMATICS

05-04 | LEGO | Monte Carlo methods | 05A16 | asymptotic enumeration | Asymptotic enumeration | MATHEMATICS

Journal Article

International Journal of Computer Mathematics, ISSN 0020-7160, 03/2014, Volume 91, Issue 3, pp. 434 - 446

Bracelets are lexicographically minimal k-ary strings symmetric under rotation and reversal. In this paper, we present an algorithm for lexicographic listing...

bracelet with fixed density | 05-04 | combinatorial generation | necklace | CAT algorithm | LYNDON WORDS | MATHEMATICS, APPLIED | NECKLACES | Mathematical models | Algorithms | Bracelets | Strings | Density | Alphabets

bracelet with fixed density | 05-04 | combinatorial generation | necklace | CAT algorithm | LYNDON WORDS | MATHEMATICS, APPLIED | NECKLACES | Mathematical models | Algorithms | Bracelets | Strings | Density | Alphabets

Journal Article

Extremes, ISSN 1386-1999, 3/2017, Volume 20, Issue 1, pp. 121 - 168

For a stochastic process {X t } t∈T with identical one-dimensional margins and upper endpoint τ up its tail correlation function (TCF) is defined through χ ( X...

Tail dependence matrix | 52B12 | Civil Engineering | Convex polytope | 52B05 | Max-stable process | 60G70 | Statistics, general | Statistics | Tawn-Molchanov model | 15B51 | 05-04 | Hydrogeology | Statistics for Business/Economics/Mathematical Finance/Insurance | Quality Control, Reliability, Safety and Risk | Tail correlation matrix | Extremal coefficient | Environmental Management | STATISTICS & PROBABILITY | RANDOM-FIELDS | DEPENDENCE | DISTRIBUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MEDIA | ERGODIC PROPERTIES | Stochastic processes | Analysis | Studies | Convex analysis | Stochastic models | Correlation | Mathematical analysis | Inequalities | Texts | Continuity | Regularity | Stemming

Tail dependence matrix | 52B12 | Civil Engineering | Convex polytope | 52B05 | Max-stable process | 60G70 | Statistics, general | Statistics | Tawn-Molchanov model | 15B51 | 05-04 | Hydrogeology | Statistics for Business/Economics/Mathematical Finance/Insurance | Quality Control, Reliability, Safety and Risk | Tail correlation matrix | Extremal coefficient | Environmental Management | STATISTICS & PROBABILITY | RANDOM-FIELDS | DEPENDENCE | DISTRIBUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MEDIA | ERGODIC PROPERTIES | Stochastic processes | Analysis | Studies | Convex analysis | Stochastic models | Correlation | Mathematical analysis | Inequalities | Texts | Continuity | Regularity | Stemming

Journal Article

Mathematical Programming Computation, ISSN 1867-2949, 3/2013, Volume 5, Issue 1, pp. 57 - 73

This paper describes implementation and computational results of a polynomial test of total unimodularity. The test is a simplified version of a prior method....

Total unimodularity | Mathematics of Computing | Operations Research/Decision Theory | Polynomial test | Mathematics | Theory of Computation | 05-04 combinatorics - explicit machine computation and programming | Optimization | Unimodularity

Total unimodularity | Mathematics of Computing | Operations Research/Decision Theory | Polynomial test | Mathematics | Theory of Computation | 05-04 combinatorics - explicit machine computation and programming | Optimization | Unimodularity

Journal Article

Computing and Visualization in Science, ISSN 1432-9360, 2/2010, Volume 13, Issue 2, pp. 99 - 110

This note wants to explain how to obtain meaningful pictures of (possibly high-dimensional) convex polytopes, triangulated manifolds, and other objects from...

Polytopes | 05C10 | Visualization | Computational Mathematics and Numerical Analysis | Simplicial manifolds | 52B11 | Mathematics | Schlegel diagrams | Tight spans of finite metric spaces | 05-04 | Algorithms | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis | Graphs | Tropical polytopes | 68R10 | Computer Applications in Chemistry

Polytopes | 05C10 | Visualization | Computational Mathematics and Numerical Analysis | Simplicial manifolds | 52B11 | Mathematics | Schlegel diagrams | Tight spans of finite metric spaces | 05-04 | Algorithms | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis | Graphs | Tropical polytopes | 68R10 | Computer Applications in Chemistry

Journal Article

Annals of Combinatorics, ISSN 0218-0006, 12/1998, Volume 2, Issue 4, pp. 365 - 385

We describe a characteristic-free algorithm for “reducing” an algebraic variety defined by the vanishing of a set of integer polynomials. In very special...

05-04 | matroids | 68Q40 | 14Q15 | computational algebra | Mathematics | Combinatorics | spanning trees | 05A15 | Algorithms | Algebra

05-04 | matroids | 68Q40 | 14Q15 | computational algebra | Mathematics | Combinatorics | spanning trees | 05A15 | Algorithms | Algebra

Journal Article

Computing, ISSN 0010-485X, 12/1987, Volume 39, Issue 4, pp. 327 - 344

We describe an implementation of a cutting plane algorithm for the minimum weight perfect 2-matching problem. This algorithm is based on Edmonds' complete...

Matching | cutting plane algorithm | AMS Subject Classifications: 05-04, 05C45, 90C10 | polyhedral combinatorics | Algorithms | Management science

Matching | cutting plane algorithm | AMS Subject Classifications: 05-04, 05C45, 90C10 | polyhedral combinatorics | Algorithms | Management science

Journal Article

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