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94 papers · 1 filter
A Pollak Proof for the Number of Weakly Increasing Parking Functions
Pamela E. Harris, J. Carlos Martínez Mori, Alexander N. Wilson
We develop a circular-street argument, in the style of Pollak, to obtain a new proof that there are weakly increasing parking functions of length…
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…
A quantum Murnaghan--Nakayama rule for the flag manifold
Carolina Benedetti, Nantel Bergeron, Laura Colmenarejo +2
In this paper, we give a rule for the multiplication of a Schubert class by a tautological class in the (small) quantum cohomology ring of the flag manifold. As an intermediate ste…
The lattice of submonoids of the uniform block permutations containing the symmetric group
Rosa Orellana, Franco Saliola, Anne Schilling +1
We study the lattice of submonoids of the uniform block permutation monoid containing the symmetric group (which is its group of units). We prove that this lattice is distributive…
From quasi-symmetric to Schur expansions with applications to symmetric chain decompositions and plethysm
Rosa Orellana, Franco Saliola, Anne Schilling +1
It is an important problem in algebraic combinatorics to deduce the Schur function expansion of a symmetric function whose expansion in terms of the fundamental quasisymmetric func…
The excedance quotient of the Bruhat order, Quasisymmetric Varieties and Temperley-Lieb algebras
Nantel Bergeron, Lucas Gagnon
Let be the ring of polynomial in variables and consider the ideal generated by quasisym…