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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
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
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
Journal Article
Advances in Computational Mathematics, ISSN 1019-7168, 4/2019, Volume 45, Issue 2, pp. 519 - 561
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
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
Journal Article
Foundations of Computational Mathematics, ISSN 1615-3375, 6/2010, Volume 10, Issue 3, pp. 303 - 338
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
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
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
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
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
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
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
Journal Article
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