6 papers · 1 filter
Polynomiality of Stretched Schubert Structure Constants and Key Coefficients
Per Alexandersson
We prove that monomial coefficients in affine families of key and Schubert polynomials are eventually polynomial. The proof combines Demazure operators with vector partition functi…
Partition division maps, symmetric functions and positivity
Per Alexandersson, Lilan Dai
We study a linear map on symmetric functions that ``divides'' a partition by a positive integer , sending a Schur function indexed by a partition of to a symmetric function…
Some Families of Type Set Partitions Counted by the Dowling Numbers
Per Alexandersson, Fufa Beyene, Roberto Mantaci
In this paper, we study type set partitions without zero block. Certain classes of these partitions, such as merging-free and separated partitions (enumerated by the Dowling nu…
Decomposing Determinantal Varieties from Statistics via Matroid Theory
Per Alexandersson, Yulia Alexandr, Emiliano Liwski +2
We study determinantal varieties from conditional independence models with hidden variables, focusing on their irreducible decompositions, dimensions, degrees, and Gröbner bases.…
A weighted Murnaghan-Nakayama rule for -partitions
Per Alexandersson, Olivia Nabawanda
The -partition generating function is a quasisymmetric function obtained from a labeled poset. Recently, Liu and Weselcouch gave a formula for the coefficien…
The mystery of plethysm coefficients
Laura Colmenarejo, Rosa Orellana, Franco Saliola +2
Composing two representations of the general linear groups gives rise to Littlewood's (outer) plethysm. On the level of characters, this poses the question of finding the Schur exp…