Publications (15)
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…
The Lehmer complex of a Bruhat interval
Davide Bolognini, Paolo Sentinelli
We introduce Lehmer codes, with immersions in the Bruhat order, for several finite Coxeter groups, including all the classical Weyl groups. This allows to associate to each lower B…
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…
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…
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…
Non-extendably shellable skeleta of simplices
Davide Bolognini, Paolo Sentinelli
We disprove a long-standing open conjecture due to Simon stating that all skeleta of simplices are extendably shellable. In particular, for every we provide a pure -d…
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…
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;…
A weak Lehmer code for type
Paolo Sentinelli, Andrea Zatti
We provide an algorithm to construct a multicomplex for any lower Bruhat interval of , such that its rank--generating function equals that of the Bruhat interval. For Weyl gro…
Wachs permutations, Bruhat order and weak order
Francesco Brenti, Paolo Sentinelli
We study the partial orders induced on Wachs and signed Wachs permutations by the Bruhat and weak orders of the symmetric and hyperoctahedral groups. We show that these orders are…
The generalized lifting property of Bruhat intervlas
Fabrizio Caselli, Paolo Sentinelli
In [E. Tsukerman and L. Williams, {\em Bruhat Interval Polytopes}, Advances in Mathematics, 285 (2015), 766-810] it is shown that every Bruhat interval of the symmetric group satis…
-Jones-Wenzl idempotents
Gaston Burrull, Nicolas Libedinsky, Paolo Sentinelli
For a prime number and any natural number we introduce, by giving an explicit recursive formula, the -Jones-Wenzl projector , an element of the…
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…
Equivalence between invariance conjectures for parabolic Kazhdan-Lusztig polynomials
Paolo Sentinelli
We prove that the combinatorial invariance conjecture for parabolic Kazhdan-Lusztig polynomials, formulated by Mario Marietti, is equivalent to its restriction to maximal quotients…
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…