26
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Counting covered fixed points and covered arcs in an involution

Pages 2625-2635 | Received 21 Aug 2022, Published online: 06 Mar 2023

References

  • C. Banderier, M. Bousquet-M_elou, A. Denise, P. Flajolet, D. Gardy, and D. Gouyou-Beauchamps, Generating functions for generating trees, Discrete Math. 246(1-3) (2002), 29–55. doi: 10.1016/S0012-365X(01)00250-3
  • M. Barnabei, F. Bonetti, N. Castronuovo, and M. Silimbani, Visibility in restricted involutions, J. Diff. Eq. and Appl. 27(4) (2021), 481–496. doi: 10.1080/10236198.2021.1912031
  • M. Barnabei, F. Bonetti, and M. Silimbani, Restricted involutions, and Motzkin paths, Adv. in Appl. Math. 47 (2011), 102–115. doi: 10.1016/j.aam.2010.05.002
  • W.Y.C. Chen, E.Y.P. Deng, R.R.X. Du, R.P. Stanley, and C.H. Yan, Crossings and nestings of matchings and partitions, Trans. Amer. Math. Soc. 359 (2007), 1555–1575. doi: 10.1090/S0002-9947-06-04210-3
  • E. Deutsch, A. Robertson, and D. Saracino, Refined restricted involutions, European J. Combin. 28 (2007), 481–498. doi: 10.1016/j.ejc.2004.09.006
  • W.M.B. Dukes, V. Jel__nek, T. Mansour, and A. Reifegerste, New equivalences for pattern avoidance for involutions, Proc. AMS 137 (2009), 457–465. doi: 10.1090/S0002-9939-08-09492-6
  • E.S. Egge, Restricted 3412-avoiding involutions, continued fractions, and Chebyshev polynomials, Adv. in Appl. Math. 33 (2004), 451–475.
  • L. Fresse, Betti numbers of Springer fibers in type A, J. Algebra 322 (2009), 2566–2579. doi: 10.1016/j.jalgebra.2009.07.008
  • L. Fresse, R. Mansour, and A. Melnikov, Unimodality of the distribution of Betti numbers for some Springer fibers, J. Algebra 391(1) (2013), 284–304. doi: 10.1016/j.jalgebra.2013.05.018
  • O. Guibert, Combinatoire des permutations á motifs exclus en liaison avec mots, cartes planaires et tableaux de Young, Ph.D. Thesis, Université Bordeaux 1, France, 1995.
  • O. Guibert and T. Mansour, Restricted 132-involutions, Sem. Lothar. Combin. 48 (2002), Article B48a.
  • Q.-H. Hou and T. Mansour, Kernel method and linear recurrence system, J. Comput. Appl. Math. 216 (2008), 227–242. doi: 10.1016/j.cam.2007.05.001
  • S. Kitaev, Patterns in Permutations and Words, Monographs in Theoretical Computer Science, Springer, Berlin/Heidelberg, 2011.
  • R. Mansour, Betti numbers of the Springer fibers over nilpotent elements in gln(C) of Jordan forms (2b, 1a-b), J. Alg. Combin. 55(3) (2022), 847–852. doi: 10.1007/s10801-021-01074-2
  • T. Mansour and M. Shattuck, Partial matchings and pattern avoidance, Appl. Anal. Discrete Math. 7 (2013), 25–50. doi: 10.2298/AADM121130023M
  • T. Mansour and M. Shattuck, Counting permutations by the number of successions within cycles, Discrete Math. 339 (2016), 1368–1376. doi: 10.1016/j.disc.2015.12.004
  • N.J. Sloane, The On-Line Encyclopedia of Integer Sequences, http://oeis.org, 2010.
  • N. Spaltenstein, Classes unipotentes et sous-groupes de Borel, Lecture Notes in Math., Vol. 946, Springer, Berlin/New York, 1982.
  • T.A. Springer, Trigonometric sums, Green functions of finite groups and representations of Weyl groups, Invent. Math. 36 (1976), 173–207. doi: 10.1007/BF01390009

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.