The Enumeration of Permutations Avoiding 3124 and 4312
Article
First Online:
Received:
- 74 Downloads
- 1 Citations
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.
Mathematics Subject Classification
05A05 05A15Keywords
permutation class simple permutation geometric grid classPreview
Unable to display preview. Download preview PDF.
References
- 1.Albert, M.H.: PermLab: software for permutation patterns. http://www.cs.otago.ac.nz/PermLab/ (2014)
- 2.Albert M.H., Atkinson M.D.: Simple permutations and pattern restricted permutations. Discrete Math. 300(1-3), 1–15 (2005)MathSciNetCrossRefMATHGoogle Scholar
- 3.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)MathSciNetCrossRefMATHGoogle Scholar
- 4.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)Google Scholar
- 5.Albert M.H., Atkinson M.D., Vatter V.: Inflations of geometric grid classes: three case studies. Australas. J. Combin. 58(1), 27–47 (2014)MathSciNetMATHGoogle Scholar
- 6.Bóna, M.: The permutation classes equinumerous to the smooth class. Electron. J. Combin. 5, #R31 (1998)Google Scholar
- 7.Brignall R., Ruškuc N., Vatter V.: Simple permutations: decidability and unavoidable substructures. Theoret. Comput. Sci. 391(1-2), 150–163 (2008)MathSciNetCrossRefMATHGoogle Scholar
- 8.Delgado, M., Linton, S., Morais, J.: Automata — a GAP package, Version 1.13. (2011)Google Scholar
- 9.Elizalde S.: The X-class and almost-increasing permutations. Ann. Combin. 15(1), 51–68 (2011)MathSciNetCrossRefMATHGoogle Scholar
- 10.Flajolet, P., Sedgewick, R.: Analytic Combinatorics. Cambridge University Press, Cambridge (2009)Google Scholar
- 11.The GAP Group. GAP – Groups, Algorithms, and Programming, Version 4.6.4. (2013)Google Scholar
- 12.Kremer D.: Permutations with forbidden subsequences and a generalized schroder number. Discrete Math. 218(1-3), 121–130 (2000)MathSciNetCrossRefMATHGoogle Scholar
- 13.Kremer D.: Postscript: “Permutations with forbidden subsequences and a generalized Schröder number”. Discrete Math. 270(1-3), 333–334 (2003)MathSciNetCrossRefMATHGoogle Scholar
- 14.Kremer D., Shiu W.C.: Finite transition matrices for permutations avoiding pairs of length four patterns. Discrete Math. 268(1-3), 171–183 (2003)MathSciNetCrossRefMATHGoogle Scholar
- 15.Le, I.: Wilf classes of pairs of permutations of length 4. Electron. J. Combin. 12, #R25 (2005)Google Scholar
- 16.Sloane, N.J.A.: The On-Line Encyclopedia of Integer Sequences. https://oeis.org/ (2015)
- 17.Vatter, V., Waton, S.: On points drawn from a circle. Electron. J. Combin. 18(1), #P223 (2011)Google Scholar
- 18.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)Google Scholar
- 19.Wikipedia. Enumerations of specific permutation classes — Wikipedia, the free encyclopedia (2015)Google Scholar
Copyright information
© Springer International Publishing 2017