Torus orbit closures and 1-strip-less-tableaux
Algebraic Combinatorics, Volume 7 (2024) no. 4, pp. 1103-1121.

We compare two formulas for the class of a generic torus orbit closure in a Grassmannian, due to Klyachko and Berget-Fink. The naturally emerging combinatorial objects are semi-standard fillings we call 1-strip-less tableaux.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.359
Classification: 10X99, 14A12, 11L05
Keywords: torus orbit, Grassmannian, Littlewood-Richardson, Young tableau

Lian, Carl 1

1 Tufts University Department of Mathematics 177 College Ave Medford, MA 02155 (USA)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
@article{ALCO_2024__7_4_1103_0,
     author = {Lian, Carl},
     title = {Torus orbit closures and 1-strip-less-tableaux},
     journal = {Algebraic Combinatorics},
     pages = {1103--1121},
     publisher = {The Combinatorics Consortium},
     volume = {7},
     number = {4},
     year = {2024},
     doi = {10.5802/alco.359},
     language = {en},
     url = {https://alco.centre-mersenne.org/articles/10.5802/alco.359/}
}
TY  - JOUR
AU  - Lian, Carl
TI  - Torus orbit closures and 1-strip-less-tableaux
JO  - Algebraic Combinatorics
PY  - 2024
SP  - 1103
EP  - 1121
VL  - 7
IS  - 4
PB  - The Combinatorics Consortium
UR  - https://alco.centre-mersenne.org/articles/10.5802/alco.359/
DO  - 10.5802/alco.359
LA  - en
ID  - ALCO_2024__7_4_1103_0
ER  - 
%0 Journal Article
%A Lian, Carl
%T Torus orbit closures and 1-strip-less-tableaux
%J Algebraic Combinatorics
%D 2024
%P 1103-1121
%V 7
%N 4
%I The Combinatorics Consortium
%U https://alco.centre-mersenne.org/articles/10.5802/alco.359/
%R 10.5802/alco.359
%G en
%F ALCO_2024__7_4_1103_0
Lian, Carl. Torus orbit closures and 1-strip-less-tableaux. Algebraic Combinatorics, Volume 7 (2024) no. 4, pp. 1103-1121. doi : 10.5802/alco.359. https://alco.centre-mersenne.org/articles/10.5802/alco.359/

[1] Berget, Andrew; Fink, Alex Equivariant Chow classes of matrix orbit closures, Transform. Groups, Volume 22 (2017) no. 3, pp. 631-643 | DOI | MR | Zbl

[2] Coskun, Izzet A Littlewood-Richardson rule for two-step flag varieties, Invent. Math., Volume 176 (2009) no. 2, pp. 325-395 | DOI | MR | Zbl

[3] Klyachko, A. A. Orbits of a maximal torus on a flag space, Funktsional. Anal. i Prilozhen., Volume 19 (1985) no. 1, pp. 77-78 | MR

[4] Klyachko, A. A. Toric varieties and flag spaces, Trudy Mat. Inst. Steklov., Volume 208 (1995), pp. 139-162 | MR

[5] Lee, Mitchell; Patel, Anand; Spink, Hunter; Tseng, Dennis Orbits in ( r ) n and equivariant quantum cohomology, Adv. Math., Volume 362 (2020), Paper no. 106951, 79 pages | DOI | MR | Zbl

[6] Lian, Carl Degenerations of complete collineations and geometric Tevelev degrees of r , 2023 | arXiv

[7] Nadeau, Philippe; Tewari, Vasu The permutahedral variety, mixed Eulerian numbers, and principal specializations of Schubert polynomials, Int. Math. Res. Not. IMRN (2023) no. 5, pp. 3615-3670 | DOI | MR | Zbl

[8] Speyer, David E A matroid invariant via the K-theory of the Grassmannian, Adv. Math., Volume 221 (2009) no. 3, pp. 882-913 | DOI | MR | Zbl

[9] Stanley, Richard P. Enumerative combinatorics. Vol. 2, Cambridge Studies in Advanced Mathematics, 208, Cambridge University Press, Cambridge, 2024, xvi+783 pages | MR

Cited by Sources: