6 papers · 1 filter
A positive combinatorial formula for the double Edelman--Greene coefficients
Jack Chen-An Chou, Tianyi Yu
Lam, Lee, and Shimozono introduced the double Stanley symmetric functions in their study of the equivariant geometry of the affine Grassmannian. They proved that the associated dou…
Grothendieck positivity for normal square root crystals
Eric Marberg, Kam Hung Tong, Tianyi Yu
Normal crystals (also known as Stembridge crystals) are commonly used to establish the Schur positivity of symmetric functions, as their characters are sums of Schur polynomials. I…
Tableau formula for vexillary double Edelman--Greene coefficients
Adam Gregory, Zachary Hamaker, Tianyi Yu
Lam, Lee and Shimozono recently introduced backstable double Grothendieck polynomials to represent -theory classes of the infinite flag variety. They used them to define double…
Marked Bumpless Pipedreams and Compatible Pairs
Daoji Huang, Mark Shimozono, Tianyi Yu
We construct a bijection between marked bumpless pipedreams with reverse compatible pairs, which are in bijection with not-necessarily-reduced pipedreams. This directly unifies var…
Embedding bumpless pipedreams as Bruhat chains
Tianyi Yu
Schubert polynomials are distinguished representatives of Schubert cycles in the cohomology of the flag variety. In the spirit of Bergeron and Sottile, we use the Bruhat order to g…
Lascoux expansion of the product of a Lascoux and a stable Grothendieck
Gidon Orelowitz, Tianyi Yu
This paper gives a tableau formula for expanding the product of a Lascoux polynomial and a stable Grothendieck polynomial into Lascoux polynomials. Lascoux and stable Grothendieck…