IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v20y2007i2d10.1007_s10959-007-0070-5.html
   My bibliography  Save this article

Normal Approximations for Descents and Inversions of Permutations of Multisets

Author

Listed:
  • Mark Conger

    (University of Michigan)

  • D. Viswanath

    (University of Michigan)

Abstract

Normal approximations for descents and inversions of permutations of the set {1,2,…,n} are well known. We consider the number of inversions of a permutation π(1),π(2),…,π(n) of a multiset with n elements, which is the number of pairs (i,j) with 1≤i π(j). The number of descents is the number of i in the range 1≤i π(i+1). We prove that, appropriately normalized, the distribution of both inversions and descents of a random permutation of the multiset approaches the normal distribution as n→∞, provided that the permutation is equally likely to be any possible permutation of the multiset and no element occurs more than α n times in the multiset for a fixed α with 0

Suggested Citation

  • Mark Conger & D. Viswanath, 2007. "Normal Approximations for Descents and Inversions of Permutations of Multisets," Journal of Theoretical Probability, Springer, vol. 20(2), pages 309-325, June.
    • Handle: RePEc:spr:jotpro:v:20:y:2007:i:2:d:10.1007_s10959-007-0070-5
    DOI: 10.1007/s10959-007-0070-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-007-0070-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-007-0070-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Byron J. T. Morgan, 1989. "Introduction to Optimization," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 152(2), pages 254-255, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fr�d�ric Abergel & Mauro Politi, 2013. "Optimizing a basket against the efficient market hypothesis," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 13-23, December.
    2. Joh, Chang-Hyeon & Arentze, Theo A. & Timmermans, Harry J. P., 1999. "Multidimensional Sequence Alignment Methods for Activity Pattern Analysis: A comparison of dynamic programming and genetic algorithms," ERSA conference papers ersa99pa279, European Regional Science Association.
    3. Giorgio Giorgi, 2021. "On Notations for Conic Hulls and Related Considerations on Tangent Cones," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 13(3), pages 1-13, June.
    4. Mohammed Bennani Dosse & Jos Berge, 2010. "Anisotropic Orthogonal Procrustes Analysis," Journal of Classification, Springer;The Classification Society, vol. 27(1), pages 111-128, March.
    5. Bennani Dosse, Mohammed & Kiers, Henk A.L. & Ten Berge, Jos M.F., 2011. "Anisotropic generalized Procrustes analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1961-1968, May.
    6. Edgardo Brigatti & Felipe Macias & Max O. Souza & Jorge P. Zubelli, 2015. "A Hedged Monte Carlo Approach to Real Option Pricing," Papers 1509.03577, arXiv.org.
    7. Chang-Hyeon Joh & Theo A Arentze & Harry J P Timmermans, 2005. "A Utility-Based Analysis of Activity Time Allocation Decisions Underlying Segmented Daily Activity–Travel Patterns," Environment and Planning A, , vol. 37(1), pages 105-125, January.
    8. A. Dax & V. P. Sreedharan, 1997. "Theorems of the Alternative and Duality," Journal of Optimization Theory and Applications, Springer, vol. 94(3), pages 561-590, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jotpro:v:20:y:2007:i:2:d:10.1007_s10959-007-0070-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.