Mahonian pairs
نویسندگان
چکیده
Article history: Received 22 January 2011 Available online xxxx
منابع مشابه
Euler-Mahonian distributions of type Bn
Adin, Brenti, and Roichman introduced the pairs of statistics (ndes, nmaj) and (fdes, fmaj). They showed that these pairs are equidistributed over the hyperoctahedral group B n , and can be considered " Euler-Mahonian " in that they generalize the Carlitz identity. Further, they asked whether there exists a bijective proof of the equidistribution of their statistics. We give such a bijection, a...
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Adin, Brenti, and Roichman introduced the pairs of statistics (ndes, nmaj) and (fdes, fmaj). They showed that these pairs are equidistributed over the hyperoctahedral group Bn, and can be considered “Euler-Mahonian” in that they generalize the Carlitz identity. Further, they asked whether there exists a bijective proof of the equidistribution of their statistics. We give such a bijection, along...
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A number of researchers studying permutation statistics on the symmetric group Sn have considered pairs (x, Y), where x is an Eulerian statistic and Y is a Mahonian statistic. Of special interest are pairs such as (des, maj), whose joint distribution on Sn is given by Carlitz’s q-Eulerian polynomials. We present a natural Eulerian statistic stc such that the pair (stc, inv) is equally distribut...
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Babson and Steingŕımsson have recently introduced seven new permutation statistics, that they conjectured were all Mahonian (i.e. equi-distributed with the number of inversions). We prove their conjecture for the first four, and also prove that the first and the fourth are even Euler-Mahonian. We use two different, in fact, opposite, techniques. For three of them we give a computer-generated pr...
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A Mahonian d-function is a Mahonian statistic that can be expressed as a linear combination of vincular pattern functions of length at most d. Babson and Steingŕımsson classified all Mahonian 3-functions up to trivial bijections and identified many of them with well-known Mahonian statistics in the literature. We prove a host of Mahonian 3-function equidistributions over permutations in Sn avoi...
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 119 شماره
صفحات -
تاریخ انتشار 2012