5 papers
Sprout Symmetric Functions: Part 1
Tewodros Amdeberhan, John Shareshian, Richard P. Stanley
A \emph{sprout sequence} is a sequence $\frakr=(R_0=1,R_1,R_2,\dots)$ of symmetric functions in the variables $\bmx=(x_1,x_2,\dots)$ over a field generated from a power series…
Hessenberg varieties of codimension one in the flag variety
Laura Escobar, Martha Precup, John Shareshian
We study geometric and topological properties of Hessenberg varieties of codimension one in the type A flag variety. Our main results: (1) give a formula for the Poincaré polynomi…
Posets of decompositions in spherical buildings
Kevin Ivan Piterman, John Shareshian, Volkmar Welker
We propose definitions of the common bases complex, the poset of decompositions, and the poset of partial decompositions for arbitrary spherical buildings. We show that the poset o…
Gamma vectors of partitioned permutohedra
Tatsuya Horiguchi, Mikiya Masuda, Takashi Sato +2
We determine that -vectors of partitioned permutohedra, thereby generalizing a result of Foata and Schützenberger. Our result is closely related to a result of Athanasiadis on…
Counting in nilpotent injectors and Carter subgroups
Stefanos Aivazidis, Maria Loukaki, John Shareshian
We investigate number-theoretic properties of the collection of nilpotent injectors or nilpotent projectors containing certain subgroups of finite soluble (or -constr…