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17 papers · 1 filter
Bilateral parking procedures
Philippe Nadeau
We introduce the class of bilateral parking procedures on the integer line. While cars try to park in the nearest available spot to their right in the classical case, we consider m…
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…
Addendum to: Mahler's method in several variables and finite automata
Colin Faverjon, Boris Adamczewski
This note is an addendum to the paper ''Mahler's method in several variables and finite automata''. It strengthens part (i) of Theorem 1.1 of the aforementioned paper.
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",…
Generalised core partitions and Diophantine equations
Olivier Brunat, Nathan Chapelier-Laget, Thomas Gerber
We study generalised core partitions arising from affine Grassmannian elements in arbitrary Dynkin type. The corresponding notion of size is given by the atomic length in the sense…