Skip to main content
Have a personal or library account? Click to login
Equivalence classes of permutations modulo descents and left-to-right maxima Cover

Equivalence classes of permutations modulo descents and left-to-right maxima

Pure Mathematics and Applications
Volume 25 (2015): Issue 1 (September 2015)
By:  and    
Open Access
|Oct 2015
References

References

  1. [1] J.-L. Baril, Statistics-preserving bijections between classical and cyclic permutations, Inform. Process. Lett., 113 (2003) 17-22.
    Open DOISearch in Google Scholar
  2. [2] J.-L. Baril, T. Mansour and A. Petrossian, Equivalence classes of permutations modulo excedances, J. Comb., 5 (2014) 453-469.
    Open DOISearch in Google Scholar
  3. [3] M. Bona, Combinatorics of permutations, Chapman and Hall/CRC, Second Edition, 2012.
    Search in Google Scholar
  4. [4] E. Deutsch and L. Shapiro, A survey of the Fine numbers, Discrete Math., 241 (2001) 241-265.
    Open DOISearch in Google Scholar
  5. [5] D. C. Foata and M. P. Schützenberger, Théorie Géométrique des Polynômes Euleriens, Lecture Notes in Math., 138, Springer-Verlag, Berlin, 1970.
    Open DOISearch in Google Scholar
  6. [6] O. Guibert, E. Pergola and R. Pinzani, Vexillary involutions are enumerated by Motzkin numbers, Ann. Comb., 5 (2001) 153-174.
    Open DOISearch in Google Scholar
  7. [7] S. Kitaev, Patterns in permutations and words, Springer-Verlag, 2011.
    Open DOISearch in Google Scholar
  8. [8] D. E. Knuth, The art of computer programming, Volume I, Addison-Wesley, Reading MA, Third edition, 1997.
    Search in Google Scholar
  9. [9] C. Krattenthaler, Permutations with restricted patterns and Dyck paths, Adv. in Appl. Math., 27 (2001) 510-530.
    Open DOISearch in Google Scholar
  10. [10] T. Mansour, Combinatorics of Set Partitions, Discrete Mathematics and its Applications, Chapman & Hall/CRC, 2013.
    Open DOISearch in Google Scholar
  11. [11] T. Mansour, Permutations avoiding a pattern from Sk and at least two patterns from S3, Ars. Combin., 62 (2002) 227-239.
    Search in Google Scholar
  12. [12] T. Mansour and A. Vainshtein, Restricted 132-avoiding permutations, Adv. Appl. Math., 26 (2001) 258-269.
    Open DOISearch in Google Scholar
  13. [13] R. Simion and F.W. Schmidt, Restricted permutations, European J. Combin., 6 (1985) 383-406.
    Open DOISearch in Google Scholar
  14. [14] J. West, Permutations with forbidden subsequences and stack-sortable permutations, Ph.D. Thesis, MIT, 1990.
    Search in Google Scholar
  15. [15] J. West, Generating trees and forbidden subsequences, Local Proceedings of FPSAC 1994, 441-450.
    Search in Google Scholar
  16. [16] J. West, Generating trees and the Catalan and Schröder numbers, Discrete Math., 146 (1995) 247-262.
    Search in Google Scholar
  17. [17] A. Sapounakis, I. Tasoulas and P. Tsikouras, Counting strings in Dyck paths, Discrete Math., 307 (2007) 2909-2924.
    Search in Google Scholar
  18. [18] N.J.A. Sloane, On-Line Encyclopedia of Integer Sequences, http://oeis.org/.
    Search in Google Scholar
  19. [19] R. P. Stanley, Enumerative Combinatorics, Volume I, Cambridge University Press, 2002.
    Search in Google Scholar
DOI: https://doi.org/10.1515/puma-2015-0002 | Journal eISSN: 1788-800X
Journal RSS Feed
Language: English
Page range: 19 - 29
Submitted on: Jul 8, 2014
Published on: Oct 7, 2015
Published by: Corvinus University of Budapest
In partnership with: Paradigm Publishing Services
Keywords:
permutation,
equivalence class,
descent,
left-to-right maximum,
pattern,
Bell number,
Motzkin number,
Catalan number,
Fine number
Related subjects:
Computer sciences,
Theoretical computer sciences,
Business and economics,
Mathematics and statistics for economists,
Mathematics,
Mathematics,
Analysis,
Differential equations and dynamical systems

© 2015 Jean-Luc Baril, Armen Petrossian, published by Corvinus University of Budapest
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 25 (2015): Issue 1 (September 2015)
Previous article
Next article