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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
Journal Article
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
Journal Article
Mathematical programming, ISSN 0025-5610, 2001, Volume 90, Issue 2, pp. 273 - 290
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
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
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
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
Journal Article
Annals of Combinatorics, ISSN 0218-0006, 12/2006, Volume 10, Issue 4, pp. 431 - 441
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
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
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
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
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
Journal Article
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