Statistics on Signed Permutations Groups ( Extended Abstract )

نویسنده

  • Michael Fire
چکیده

Abstract. A classical result of MacMahon shows that the length function and the major index are equidistributed over the symmetric groups. Through the years this result was generalized in various ways to signed permutation groups. In this paper we present several new generalizations, in particular, we study the effect of different linear orders on the letters [−n, n] and generalize a classical result of Foata and Zeilberger.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

MacMahon-type Identities for Signed Even Permutations

MacMahon’s classic theorem states that the length and major index statistics are equidistributed on the symmetric group Sn. By defining natural analogues or generalizations of those statistics, similar equidistribution results have been obtained for the alternating group An by Regev and Roichman, for the hyperoctahedral group Bn by Adin, Brenti and Roichman, and for the group of even-signed per...

متن کامل

Perfect sorting by reversals is not always difficult ( Extended abstract ? )

This paper investigates the problem of conservation of combinatorial structures in genome rearrangement scenarios. We characterize a class of signed permutations for which one can compute in polynomial time a reversal scenario that conserves all common intervals, and that is parsimonious among such scenarios. The general problem is believed to be NP-hard. We show that there exists a class of pe...

متن کامل

Consensus Ranking with Signed Permutations

Signed permutations (also known as the hyperoctahedral group) are used in modeling genome rearrangements. The algorithmic problems they raise are computationally demanding when not NP-hard. This paper presents a tractable algorithm for learning consensus ranking between signed permutations under the inversion distance. This can be extended to estimate a natural class of exponential models over ...

متن کامل

Signed Words and Permutations II; The Euler-Mahonian Polynomials

As for the symmetric group of ordinary permutations there is also a statistical study of the group of signed permutations, that consists of calculating multivariable generating functions for this group by statistics involving record values and the length function. Two approaches are here systematically explored, using the flag-major index on the one hand, and the flag-inversion number on the ot...

متن کامل

Combinatorics in the group of parity alternating permutations

We call a permutation parity alternating, if its entries assume even and odd integers alternately. Parity alternating permutations form a subgroup of the symmetric group. This paper deals with such permutations classified by two permutation statistics; the numbers of ascents and inversions. It turns out that they have a close relationship to signed Eulerian numbers. The approach is based on a s...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2006