Abstract
A prism tableau is a set of reverse semistandard tableaux, each positioned within an ambient grid. Prism tableaux were introduced in joint work with A. Yong to provide a formula for the Schubert polynomials of A. Lascoux and M.-P. Schützenberger. This formula directly generalizes the well known expression for Schur polynomials as a sum over semistandard tableaux. Alternating sign matrix varieties generalize the matrix Schubert varieties of W. Fulton. We use prism tableaux to give a formula for the multidegree of an alternating sign matrix variety.
| Original language | English (US) |
|---|---|
| State | Published - 2018 |
| Externally published | Yes |
| Event | 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 - Hanover, United States Duration: Jul 16 2018 → Jul 20 2018 |
Conference
| Conference | 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 |
|---|---|
| Country/Territory | United States |
| City | Hanover |
| Period | 7/16/18 → 7/20/18 |
Bibliographical note
Funding Information:I thank my advisor, Alexander Yong, for his guidance throughout this project. I also thank Allen Knutson for suggesting this direction of research and Jessica Striker for helpful conversations about alternating sign matrices. I was supported by a UIUC Campus Research Board and by an NSF Grant. This work was partially completed while participating in the trimester “Combinatorics and Interactions” at the Institut Henri Poincaré. My travel support was provided by NSF Conference Grant 1643027. I was funded by the Ruth V. Shaff and Genevie I. Andrews Fellowship. I used Sage and Macaulay2 during the course of my research.
Publisher Copyright:
© FPSAC 2018 - 30th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.
Keywords
- Alternating sign matrices
- Prism tableaux
- Schubert polynomials