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Grove polynomials and -theoretic quasisymmetry
Philippe Nadeau, Hunter Spink, Vasu Tewari
We define the grove polynomials, a set-valued extension of forest polynomials. We show that they are -theoretically dual to the quasisymmetric Schubert cells which pave the quas…
Richardson tableaux and Schubert positivity
Hunter Spink, Vasu Tewari
We compute the Schubert cycle expansion of those irreducible components of Springer fibers equal to Richardson varieties. This generalizes work of Güemes in the case of a hook shap…
Equivariant quasisymmetry and noncrossing partitions
Nantel Bergeron, Lucas Gagnon, Philippe Nadeau +2
We introduce a definition of ``equivariant quasisymmetry'' for polynomials in two sets of variables. Using this definition we define quasisymmetric generalizations of the theory of…
Schubert polynomial expansions revisited
Philippe Nadeau, Hunter Spink, Vasu Tewari
We give an elementary approach utilizing only the divided difference formalism for obtaining expansions of Schubert polynomials that are manifestly nonnegative, by studying solutio…
Quasisymmetric divided differences
Philippe Nadeau, Hunter Spink, Vasu Tewari
We develop a quasisymmetric analogue of the combinatorial theory of Schubert polynomials and the associated divided difference operators. Our counterparts are "forest polynomials",…
Tutte polynomials in superspace
Brendon Rhoades, Vasu Tewari, Andy Wilson
We associate a quotient of superspace to any hyperplane arrangement by considering the differential closure of an ideal generated by powers of certain homogeneous linear forms. Thi…