3 citations · 6 across the 9 of their papers we have counts for
9 papers
The Lehmer complex of a Bruhat interval
Davide Bolognini, Paolo Sentinelli
We introduce Lehmer codes for several finite Coxeter groups, including all classical Weyl groups. These codes correspond to embed products of chains in the Bruhat order, which allo…
Reflections and quotients in Coxeter groups
Paolo Sentinelli
We present a formula relating the set of left descents of an element of a Coxeter group with the sets of left descents of its projections on maximal quotients indexed by simple rig…
Linearly shellable complexes
Paolo Sentinelli
We introduce the class of linearly shellable pure simplicial complexes. The characterizing property is the existence of a labeling of their vertices such that all linear extensions…
Linear extensions and shelling orders
Davide Bolognini, Paolo Sentinelli
We prove that linear extensions of the Bruhat order of a matroid are shelling orders and that the barycentric subdivision of a matroid is a Coxeter matroid, viewing barycentric sub…
Immanant varieties
Davide Bolognini, Paolo Sentinelli
We introduce immanant varieties, associated to simple characters of a finite group. They include well-studied classes of varieties, as Segre embeddings, Grassmannians and certain o…
The intermediate orders of a Coxeter group
Angela Carnevale, Matthew Dyer, Paolo Sentinelli
We define a class of partial orders on a Coxeter group associated with sets of reflections. In special cases, these lie between the left weak order and the Bruhat order. We prove t…
P-flag spaces and incidence stratifications
Davide Bolognini, Paolo Sentinelli
For any finite poset P we introduce a homogeneous space as a quotient of the general linear group with the incidence group of P. When P is a chain this quotient is a flag variety;…
Parabolically induced functions and equidistributed pairs
Paolo Sentinelli
Given a function defined over a parabolic subgroup of a Coxeter group, equidistributed with the length, we give a procedure to construct a function over the entire group, equidistr…
Artin group injection in the Hecke algebra for right-angled groups
Paolo Sentinelli
We prove some injectivity results: that a Coxeter monoid -algebra (or -Hecke algebra) injects in the incidence -algebra of the corresponding Bruhat poset…