Expected Number of Inversions After a Sequence of Random Adjacent Transpositions

Henrik Eriksson, Kimmo Eriksson () and Jonas Sjöstrand
Additional contact information
Henrik Eriksson: NADA, KTH
Kimmo Eriksson: IMa, Mälardalens högskola

A chapter in Formal Power Series and Algebraic Combinatorics, 2000, pp 677-685 from Springer

Abstract: Abstract We give expressions for the expected number of inversions after t random adjacent transpositions have been performed on the identity permutation in S n + 1 The problem is a simplification of a problem motivated by genome evolution. For a fixed t and for all n ≥ t, the expected number of inversions after t random adjacent transpositions is $${E_{nt}} = t - \frac{2}{n}(\begin{array}{*{20}{c}} t\\ 2 \end{array}) + r = \sum\limits_{r = 2}^t {\frac{{{{( - 1)}^r}}}{{{n^r}}}} [{2^r}{C_r}(\begin {array}{*{20}{c}} t\\ {r + 1} \end{array}) + 4{d_r}(\begin{array}{*{20}{c}} t \\ r\end{array})],$$ where d 2 = 0, d 3 = 1, d 4 = 9, d 5 = 69,... is a certain integer sequence. An important part of the our method is the use of a heat conduction analogy of the random walks, which guarantees certain properties of the solution.

Keywords: Cayley Graph; Grid Graph; Identity Permutation; Finite Case; Adjacent Transposition (search for similar items in EconPapers)
Date: 2000
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-04166-6_66

Ordering information: This item can be ordered from
http://www.springer.com/9783662041666

DOI: 10.1007/978-3-662-04166-6_66

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().