Major indices, Mahonian identities and ordered generating systems (extended abstract)

Robert Shwartz

Major indices, Mahonian identities and ordered generating systems (extended abstract)

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Abstract

A classical result of MacMahon shows that the length function and the major index are equidistributed over the symmetric group. A long standing open problem is to extend the notion of major index and MacMahon identity to other groups. A partial solution was given in [3] and [5], where this result was extended to classical Weyl groups. In this paper, it is proved that various permutation groups may be decomposed into a set-wise direct product of cyclic subgroups. This property is then used to extend the notion of major index and MacMahon identity to these groups.

Original language	English
State	Published - 2007
Externally published	Yes
Event	19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 - Tianjin, China Duration: 2 Jul 2007 → 6 Jul 2007

Conference

Conference	19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07
Country/Territory	China
City	Tianjin
Period	2/07/07 → 6/07/07

Cite this

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abstract = "A classical result of MacMahon shows that the length function and the major index are equidistributed over the symmetric group. A long standing open problem is to extend the notion of major index and MacMahon identity to other groups. A partial solution was given in [3] and [5], where this result was extended to classical Weyl groups. In this paper, it is proved that various permutation groups may be decomposed into a set-wise direct product of cyclic subgroups. This property is then used to extend the notion of major index and MacMahon identity to these groups.",

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N2 - A classical result of MacMahon shows that the length function and the major index are equidistributed over the symmetric group. A long standing open problem is to extend the notion of major index and MacMahon identity to other groups. A partial solution was given in [3] and [5], where this result was extended to classical Weyl groups. In this paper, it is proved that various permutation groups may be decomposed into a set-wise direct product of cyclic subgroups. This property is then used to extend the notion of major index and MacMahon identity to these groups.

AB - A classical result of MacMahon shows that the length function and the major index are equidistributed over the symmetric group. A long standing open problem is to extend the notion of major index and MacMahon identity to other groups. A partial solution was given in [3] and [5], where this result was extended to classical Weyl groups. In this paper, it is proved that various permutation groups may be decomposed into a set-wise direct product of cyclic subgroups. This property is then used to extend the notion of major index and MacMahon identity to these groups.

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T2 - 19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07

Y2 - 2 July 2007 through 6 July 2007

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Major indices, Mahonian identities and ordered generating systems (extended abstract)

Abstract

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