THESIS
2019
vii, 82 leaves : illustrations ; 30 cm
Abstract
We study families of symmetric functions F̂
_{z} indexed by affine involutions z and F̂
_{z}^{FPF} indexed
by affine fixed-point-free involutions z. These power series are analogues of Lam's affine
Stanley symmetric functions and generalizations of the (fixed-point-free) involution Stanley
symmetric functions introduced by Hamaker, Marberg, and Pawlowski. Our main result is to
prove transition formulas for these two families of symmetric functions which can be used to
define an affine (fixed-point-free) involution analogues of the Lascoux-Schützenberger tree.
Our proof of these two formulas is based on Lam and Shimozono's transition formula for
affine Stanley symmetric functions and the property that affine fixed-point-free involutions
form a quasiparabolic set as introduced by Rains and...[
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We study families of symmetric functions F̂
_{z} indexed by affine involutions z and F̂
_{z}^{FPF} indexed
by affine fixed-point-free involutions z. These power series are analogues of Lam's affine
Stanley symmetric functions and generalizations of the (fixed-point-free) involution Stanley
symmetric functions introduced by Hamaker, Marberg, and Pawlowski. Our main result is to
prove transition formulas for these two families of symmetric functions which can be used to
define an affine (fixed-point-free) involution analogues of the Lascoux-Schützenberger tree.
Our proof of these two formulas is based on Lam and Shimozono's transition formula for
affine Stanley symmetric functions and the property that affine fixed-point-free involutions
form a quasiparabolic set as introduced by Rains and Vazirani.
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