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arXiv · 1312.7687

The maximum cardinality of minimal inversion complete sets in finite reflection groups

Claudia Malvenuto·Pierluigi Möseneder Frajria·Luigi Orsina·Paolo Papi
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Abstract

We compute for reflection groups of type $A,B,D,F_4,H_3$ and for dihedral groups a statistic counting the maximal cardinality of a set of elements in the group whose generalized inversions yield the full set of inversions and which are minimal with respect to this property. We also provide lower bounds for the $E$ types that we conjecture to be the exact value of our statistic.

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Claudia Malvenuto, Pierluigi Möseneder Frajria, Luigi Orsina, Paolo Papi. 2013-12-30. The maximum cardinality of minimal inversion complete sets in finite reflection groups. https://arxiv.org/abs/1312.7687

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