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Proceedings of the London Mathematical Society, ISSN 0024-6115, 10/2019, Volume 119, Issue 4, pp. 960 - 997
We establish that there is an algebraic number ξ≈2.30522 such that while there are uncountably many growth rates of permutation classes arbitrarily close to ξ,... 
05A05 | 05A16 (primary) | 05A15 (secondary)
Journal Article
The American Mathematical Monthly, ISSN 0002-9890, 10/2019, Volume 126, Issue 9, pp. 840 - 840
Journal Article
Glasgow Mathematical Journal, ISSN 0017-0895, 2019, Volume 62, Issue 1, pp. 93 - 107
AbstractWe show that for any n and q, the number of real conjugacy classes in $ \rm{PGL}(\it{n},\mathbb{F}_q) $ is equal to the number of real conjugacy... 
2010 Mathematics Subject Classification | 20G40 | 05A15 | 20E45
Journal Article
The American Mathematical Monthly, ISSN 0002-9890, 05/2018, Volume 125, Issue 5, pp. 447 - 452
We give results for partitions of the set of the first n natural numbers into k nonempty subsets S 1 , S 2 , ..., S k with respect to the number of isolated... 
Secondary 05A15; 05A19 | Primary 05A18 | MATHEMATICS | 05A19 | Secondary 05A15
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 08/2019, Volume 119, Issue 2, pp. 358 - 378
We present the first combinatorial scheme for counting labelled 4‐regular planar graphs through a complete recursive decomposition. More precisely, we show... 
05C30 (primary) | 05A15 | 05C10 (secondary) | MATHEMATICS | Mathematics - Combinatorics
Journal Article
Annals of Combinatorics, ISSN 0218-0006, 11/2014, Volume 18, Issue 4, pp. 579 - 583
Journal Article
DUKE MATHEMATICAL JOURNAL, ISSN 0012-7094, 07/2012, Volume 161, Issue 10, pp. 1817 - 1862
Inspired by Feynman integral computations in quantum field theory, Kontsevich conjectured in 1997 that the number of points of graph hypersurfaces over a... 
POLYNOMIALS | MATHEMATICS | FEYNMAN GRAPHS | MOTIVES | 14M12 | 14G10 | 11G25 | 05A15 | 81T18
Journal Article
Combinatorica, ISSN 0209-9683, 8/2019, Volume 39, Issue 4, pp. 779 - 811
We determine the asymptotic number of index n subgroups in virtually cyclic Coxeter groups and their free products as n → ∞. 
Mathematics, general | 20E07 | Mathematics | Combinatorics | 05A15 | 20F55 | Group Theory
Journal Article
SpringerPlus, ISSN 2193-1801, 12/2016, Volume 5, Issue 1, pp. 1 - 18
We introduce and study k-commuting permutations. One of our main results is a characterization of permutations that k-commute with a given permutation. Using... 
Hamming metric | Commutation relation | Enumeration | Science, Humanities and Social Sciences, multidisciplinary | Symmetric group | 20B30 | Primary 05A05 | Secondary 05A15 | CODES | MATRICES | MULTIDISCIPLINARY SCIENCES | Mathematics - Combinatorics
Journal Article
Combinatorica, ISSN 0209-9683, 4/2015, Volume 35, Issue 3, pp. 309 - 315
Many recurrences that occur in combinatorics incorporate linear and self-convolutive terms. The generating function associated to these is usually not well... 
Mathematics, general | Mathematics | 30E20 | Combinatorics | 05A15 | 11B37 | MATHEMATICS
Journal Article
Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 08/2015, Volume 77, pp. 1 - 5
In this paper, we introduce ( ) − Fibonacci quaternion polynomials that generalize the − Fibonacci quaternion numbers, which in their turn are a generalization... 
11B39 | 11R52 | 05A15 | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | GENERALIZED FIBONACCI | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | K-FIBONACCI
Journal Article
The American Mathematical Monthly, ISSN 0002-9890, 08/2018, Volume 125, Issue 7, pp. 659 - 659
Journal Article
The American Mathematical Monthly, ISSN 0002-9890, 04/2018, Volume 125, Issue 4, pp. 306 - 319
We investigate the following puzzle and several variations, some of which have quite surprising answers. Alice and Bob are in prison under the care of warden... 
Primary 91A28 | Secondary 05A15; 05D99 | MATHEMATICS
Journal Article
Annals of Combinatorics, ISSN 0218-0006, 3/2019, Volume 23, Issue 1, pp. 207 - 217
Enumeration problems related to words avoiding patterns as well as permutations that contain the pattern 123 exactly once have been studied in great detail.... 
Enumeration | Generating functions | Pattern in words | Mathematics | Combinatorics | 05A05 | 05A15
Journal Article
Pure Mathematics and Applications, ISSN 1788-800X, 10/2019, Volume 28, Issue 1, pp. 14 - 69
This paper basically completes a project to enumerate permutations avoiding a triple of 4-letter patterns, in the sense of classical pattern avoidance, for... 
generating function | Wilf-equivalence | 05A05 | 05A15 | pattern avoidance | INSENC algorithm
Journal Article
The American Mathematical Monthly, ISSN 0002-9890, 09/2019, Volume 126, Issue 8, pp. 735 - 739
The following question has been considered by several mathematicians over the last half century: How many incongruent triangles with integer sides have... 
Primary 05A15 | Secondary 05A18 | MATHEMATICS
Journal Article
Discrete Mathematics and Theoretical Computer Science, ISSN 1365-8050, 04/2018, Volume 19, Issue 2
Two mesh patterns are coincident if they are avoided by the same set of permutations, and are Wilf-equivalent if they have the same number of avoiders of each... 
Permutations | Coincidences | Equivalence | Classification | 05A05, 05A15 | Mathematics - Combinatorics
Journal Article
European Journal of Combinatorics, ISSN 0195-6698, 03/2017, Volume 61, pp. 242 - 275
We study nearest-neighbors walks on the two-dimensional square lattice, that is, models of walks on defined by a fixed step set that is a subset of the... 
MATHEMATICS | SINGULARITY ANALYSIS | LATTICE PATH ENUMERATION | D-FINITE | COUNTING WALKS | ALGORITHM | Mathematics | Combinatorics | Symbolic Computation | Computer Science
Journal Article
ISSN 1365-8050, 2018
Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the... 
05A05, 05A15, 05A16, 60C05 | Mathematics - Probability | Mathematics - Combinatorics
Journal Article
Algebra universalis, ISSN 0002-5240, 12/2019, Volume 80, Issue 4, pp. 1 - 19
We show that every quasitrivial n-ary semigroup is reducible to a binary semigroup, and we provide necessary and sufficient conditions for such a reduction to... 
16B99 | Algebra | 20N15 | Reducibility | Enumeration | 20M14 | Quasitrivial polyadic semigroup | Mathematics | 05A15 | Symmetry
Journal Article
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