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arXiv · 1403.4283

A poset view of the major index

Richard Ehrenborg·Margaret Readdy
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Abstract

We introduce the Major MacMahon map and show how this map interacts with the pyramid and bipyramid operators. When the Major MacMahon map is applied to the ab-index of a simplicial poset, it yields the q-analogue of n! times the h-polynomial of the poset. Applying the map to the Boolean algebra gives the distribution of the major index on the symmetric group, a seminal result due to MacMahon. Similarly, when applied to the cross-polytope we obtain the distribution of one of the major indexes on signed permutations due to Reiner.

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Richard Ehrenborg, Margaret Readdy. 2014-09-29. A poset view of the major index. https://doi.org/10.1016/j.aam.2014.09.005

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