The sorting index and inversion number on order ideals of permutation groups

Fan, Neil J. Y.; He, Liao; Li, Teresa X.S.; Zhao, Alina F. Y.

doi:10.1016/j.disc.2016.04.015

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2018

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“…We mention also that recently the question "When are sor and inv equidistributed on order ideals of the Bruhat order?" was recently addressed in [4].…”

Section: Preliminaries and Main Resultsmentioning

confidence: 99%

Graphical Mahonian Statistics on Words

Grady

Poznanović

2018

Electron. J. Combin.

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Foata and Zeilberger defined the graphical major index, maj ′ U , and the graphical inversion index, inv ′ U , for words. These statistics are a generalization of the classical permutation statistics maj and inv indexed by directed graphs U . They showed that maj ′ U and inv ′ U are equidistributed over all rearrangement classes if and only if U is bipartitional. In this paper we strengthen their result by showing that if maj ′ U and inv ′ U are equidistributed on a single rearrangement class then U is essentially bipartitional. Moreover, we define a graphical sorting index, sor ′ U , which generalizes the sorting index of a permutation. We then characterize the graphs U for which sor ′ U is equidistributed with inv ′ U and maj ′ U on a single rearrangement class.

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“…We mention also that recently the question "When are sor and inv equidistributed on order ideals of the Bruhat order?" was recently addressed in [4].…”

Section: Preliminaries and Main Resultsmentioning

confidence: 99%

Graphical Mahonian Statistics on Words

Grady

Poznanović

2018

Electron. J. Combin.

View full text Add to dashboard Cite

show abstract

The sorting index and inversion number on order ideals of permutation groups

Cited by 1 publication

References 13 publications

Graphical Mahonian Statistics on Words

Graphical Mahonian Statistics on Words

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