Abstract
We find the generating function for the class of all permutations that avoid the patterns 3124 and 4312 by showing that it is an inflation of the union of two geometric grid classes.
Similar content being viewed by others
References
Albert, M.H.: PermLab: software for permutation patterns. http://www.cs.otago.ac.nz/PermLab/ (2014)
Albert M.H., Atkinson M.D.: Simple permutations and pattern restricted permutations. Discrete Math. 300(1-3), 1–15 (2005)
Albert M.H., Atkinson M.D., Bouvel M., Ruškuc N., Vatter V.: Geometric grid classes of permutations. Trans. Amer. Math. Soc. 365(11), 5859–5881 (2013)
Albert, M.H., Atkinson, M.D., Brignall, R.: The enumeration of three pattern classes using monotone grid classes. Electron. J. Combin. 19(3), #P20 (2012)
Albert M.H., Atkinson M.D., Vatter V.: Inflations of geometric grid classes: three case studies. Australas. J. Combin. 58(1), 27–47 (2014)
Bóna, M.: The permutation classes equinumerous to the smooth class. Electron. J. Combin. 5, #R31 (1998)
Brignall R., Ruškuc N., Vatter V.: Simple permutations: decidability and unavoidable substructures. Theoret. Comput. Sci. 391(1-2), 150–163 (2008)
Delgado, M., Linton, S., Morais, J.: Automata — a GAP package, Version 1.13. (2011)
Elizalde S.: The X-class and almost-increasing permutations. Ann. Combin. 15(1), 51–68 (2011)
Flajolet, P., Sedgewick, R.: Analytic Combinatorics. Cambridge University Press, Cambridge (2009)
The GAP Group. GAP – Groups, Algorithms, and Programming, Version 4.6.4. (2013)
Kremer D.: Permutations with forbidden subsequences and a generalized schroder number. Discrete Math. 218(1-3), 121–130 (2000)
Kremer D.: Postscript: “Permutations with forbidden subsequences and a generalized Schröder number”. Discrete Math. 270(1-3), 333–334 (2003)
Kremer D., Shiu W.C.: Finite transition matrices for permutations avoiding pairs of length four patterns. Discrete Math. 268(1-3), 171–183 (2003)
Le, I.: Wilf classes of pairs of permutations of length 4. Electron. J. Combin. 12, #R25 (2005)
Sloane, N.J.A.: The On-Line Encyclopedia of Integer Sequences. https://oeis.org/ (2015)
Vatter, V., Waton, S.: On points drawn from a circle. Electron. J. Combin. 18(1), #P223 (2011)
Waton, S.: On permutation classes defined by token passing networks, gridding matrices and pictures: three flavours of involvement. PhD thesis, Univ. of St Andrews, St Andrews (2007)
Wikipedia. Enumerations of specific permutation classes — Wikipedia, the free encyclopedia (2015)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pantone, J. The Enumeration of Permutations Avoiding 3124 and 4312. Ann. Comb. 21, 293–315 (2017). https://doi.org/10.1007/s00026-017-0352-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00026-017-0352-2