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Permutations avoiding 1324 and patterns in Łukasiewicz paths

David Bevan
2015 Journal of the London Mathematical Society  
In this context, we consider occurrences of patterns in Łukasiewicz paths and prove that in the limit they exhibit a concentrated Gaussian distribution.  ...  The class Av(1324), of permutations avoiding the pattern 1324, is one of the simplest sets of combinatorial objects to define that has, thus far, failed to reveal its enumerative secrets.  ...  He is also grateful to Robert Brignall and an anonymous referee both of whom provided useful feedback which helped to improve the presentation. S.D.G.  ... 
doi:10.1112/jlms/jdv020 fatcat:6ekyuwpgozbd3nejx2mozy6o7m

On the growth of permutation classes [article]

David Bevan
2015 arXiv   pre-print
In the process, we prove that, asymptotically, patterns in Łukasiewicz paths exhibit a concentrated Gaussian distribution.  ...  We conclude by using this approach to provide an improved lower bound on the growth rate of the class of permutations avoiding the pattern 1324.  ...  In particular, we investigate the distribution of patterns in Łukasiewicz paths.  ... 
arXiv:1506.06688v1 fatcat:jgznt4crvrdt5dcjqiaelwdo5m

Catalan and Schröder permutations sortable by two restricted stacks

Jean-Luc Baril, Giulio Cerbai, Carine Khalil, Vincent Vajnovszki
2021 Information Processing Letters  
In this work we study pattern avoiding machines where the first stack avoids a pair of patterns of length 3 and investigate those pairs for which sortable permutations are counted by the (binomial transform  ...  They consist of two restricted stacks in series, ruled by a right-greedy procedure and the stacks avoid some specified patterns.  ...  Acknowledgements The authors are grateful to the anonymous referees for carefully reading the manuscript and providing many useful suggestions.  ... 
doi:10.1016/j.ipl.2021.106138 fatcat:4dzwdjupb5gunk72rctlft6jwe

The permutation classes Av(1234,2341) and Av(1243,2314) [article]

David Bevan
2015 arXiv   pre-print
We investigate the structure of the two permutation classes defined by the sets of forbidden patterns 1234,2341 and 1243,2314.  ...  By considering how the Hasse graphs of permutations in these classes can be built from a sequence of rooted source graphs, we determine their algebraic generating functions.  ...  Acknowledgements Michael Albert's PermLab software [1] was of particular benefit in helping to visualise and explore the structure of permutations in the two permutation classes.  ... 
arXiv:1407.0570v3 fatcat:tmh7nwf7tzfmnouyj4diaoqldu

On The Growth Of Permutation Classes

David Ian Bevan
2015
In the process, we prove that, asymptotically, patterns in Łukasiewicz paths exhibit a concentrated Gaussian distribution.  ...  We conclude by using this approach to provide an improved lower bound on the growth rate of the class of permutations avoiding the pattern 1324.  ...  In particular, we investigate the distribution of patterns in Łukasiewicz paths.  ... 
doi:10.21954/ou.ro.0000ab63 fatcat:ortxqdkglvdtlce5cdvm5btfjy

Generating functions for generating trees

Cyril Banderier, Mireille Bousquet-Mélou, Alain Denise, Philippe Flajolet, Danièle Gardy, Dominique Gouyou-Beauchamps
2002 Discrete Mathematics  
made in the construction of the object.  ...  Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices  ...  Acknowledgements We thank Elisa Pergola and Renzo Pinzani who presented us the problem we deal with in this paper. We are also very grateful for helpful discussions with Jean-Paul Allouche.  ... 
doi:10.1016/s0012-365x(01)00250-3 fatcat:rtnrafnddvaihmdt56kspq7g5e