The sorting index and equidistribution of set-valued statistics over restricted permutations
نویسندگان
چکیده
منابع مشابه
New permutation coding and equidistribution of set-valued statistics
A new coding for permutations is explicitly constructed and its association with the classical Lehmer coding provides a bijection of the symmetric group onto itself serving to show that six bivariable set-valued statistics are equidistributed on that group. This extends a recent result due to Cori valid for integer-valued statistics.
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We prove that the Mahonian-Stirling pairs of permutation statistics (sor, cyc) and (inv, rlmin) are equidistributed on the set of permutations that correspond to arrangements of n non-atacking rooks on a fixed Ferrers board with n rows and n columns. The proofs are combinatorial and use bijections between matchings and Dyck paths and a new statistic, sorting index for matchings, that we define....
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The inversion number and the major index are equidis-tributed on the symmetric group. This is a classical result, first proved by MacMahon [Mac15], then by Foata by means of a combinatorial bijection [Fo68]. Ever since many refinements have been derived, which consist of adding new statistics, or replacing integral-valued statistics by set-valued ones. See the works by Foata-Schützenberger [FS7...
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We compute the joint distribution of descent and major index over permutations of {1, . . . , n} with no descents in positions {n− i, n− i+ 1, . . . , n− 1} for fixed i ≥ 0. This was motivated by the problem of enumerating symmetrically constrained compositions and generalizes Carlitz’s q-Eulerian polynomial.
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A multi-break rearrangement generalizes most of genome rearrangements, such as block-interchanges, transpositions and reversals. A k-break cuts k adjacencies over a permutation, and forms k new adjacencies by joining the extremities according to an arbitrary matching. Block-interchange distance is a polynomial problem, but the transposition and the reversal distances are both NP-hard problems. ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2014
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2014.03.007