Browse issues
no. 5
Vexillary signed permutations revisited
Anderson, David1; Fulton, William2
1 Department of Mathematics The Ohio State University Columbus, Ohio 43210, USA
2 Department of Mathematics University of Michigan Ann Arbor, Michigan 48109, USA
Algebraic Combinatorics, Volume 3 (2020) no. 5, pp. 1041-1057.

We study the combinatorial properties of vexillary signed permutations, which are signed analogues of the vexillary permutations first considered by Lascoux and Schützenberger. We give several equivalent characterizations of vexillary signed permutations, including descriptions in terms of essential sets and pattern avoidance, and we relate them to the vexillary elements introduced by Billey and Lam.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.122
Classification: 05E15, 05A05, 14M15
Keywords: Signed permutation, vexillary permutation, degeneracy locus, essential set.

Anderson, David 1; Fulton, William 2

1 Department of Mathematics The Ohio State University Columbus, Ohio 43210, USA
2 Department of Mathematics University of Michigan Ann Arbor, Michigan 48109, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
@article{ALCO_2020__3_5_1041_0,
     author = {Anderson, David and Fulton, William},
     title = {Vexillary signed permutations revisited},
     journal = {Algebraic Combinatorics},
     pages = {1041--1057},
     publisher = {MathOA foundation},
     volume = {3},
     number = {5},
     year = {2020},
     doi = {10.5802/alco.122},
     language = {en},
     url = {https://alco.centre-mersenne.org/articles/10.5802/alco.122/}
}
TY  - JOUR
AU  - Anderson, David
AU  - Fulton, William
TI  - Vexillary signed permutations revisited
JO  - Algebraic Combinatorics
PY  - 2020
SP  - 1041
EP  - 1057
VL  - 3
IS  - 5
PB  - MathOA foundation
UR  - https://alco.centre-mersenne.org/articles/10.5802/alco.122/
DO  - 10.5802/alco.122
LA  - en
ID  - ALCO_2020__3_5_1041_0
ER  - 
%0 Journal Article
%A Anderson, David
%A Fulton, William
%T Vexillary signed permutations revisited
%J Algebraic Combinatorics
%D 2020
%P 1041-1057
%V 3
%N 5
%I MathOA foundation
%U https://alco.centre-mersenne.org/articles/10.5802/alco.122/
%R 10.5802/alco.122
%G en
%F ALCO_2020__3_5_1041_0
Anderson, David; Fulton, William. Vexillary signed permutations revisited. Algebraic Combinatorics, Volume 3 (2020) no. 5, pp. 1041-1057. doi : 10.5802/alco.122. https://alco.centre-mersenne.org/articles/10.5802/alco.122/

[1] Anderson, David Diagrams and essential sets for signed permutations, Electron. J. Combin., Volume 25 (2018) no. 3, Paper no. 3.46, 23 pages | MR | Zbl

[2] Anderson, David; Fulton, William Degeneracy loci, Pfaffians, and vexillary signed permutations in types B, C, and D (2012) (https://arxiv.org/abs/1210.2066)

[3] Anderson, David; Fulton, William Chern class formulas for classical-type degeneracy loci, Compos. Math., Volume 154 (2018) no. 8, pp. 1746-1774 | DOI | MR | Zbl

[4] Billey, Sara Transition equations for isotropic flag manifolds, Discrete Math., Volume 193 (1998) no. 1-3, pp. 69-84 Selected papers in honor of Adriano Garsia (Taormina, 1994) | DOI | MR | Zbl

[5] Billey, Sara; Haiman, Mark Schubert polynomials for the classical groups, J. Amer. Math. Soc., Volume 8 (1995) no. 2, pp. 443-482 | DOI | MR | Zbl

[6] Billey, Sara; Lam, Tao Kai Vexillary elements in the hyperoctahedral group, J. Algebraic Combin., Volume 8 (1998) no. 2, pp. 139-152 | DOI | MR | Zbl

[7] Björner, Anders; Brenti, Francesco Combinatorics of Coxeter groups, Graduate Texts in Mathematics, 231, Springer, New York, 2005, xiv+363 pages | MR | Zbl

[8] Egge, Eric S. Enumerating rc-invariant permutations with no long decreasing subsequences, Ann. Comb., Volume 14 (2010) no. 1, pp. 85-101 | DOI | MR | Zbl

[9] Eriksson, Kimmo; Linusson, Svante Combinatorics of Fulton’s essential set, Duke Math. J., Volume 85 (1996) no. 1, pp. 61-76 | DOI | MR | Zbl

[10] Fomin, Sergey; Kirillov, Anatol N. Combinatorial B n -analogues of Schubert polynomials, Trans. Amer. Math. Soc., Volume 348 (1996) no. 9, pp. 3591-3620 | DOI | MR | Zbl

[11] Fulton, William Flags, Schubert polynomials, degeneracy loci, and determinantal formulas, Duke Math. J., Volume 65 (1992) no. 3, pp. 381-420 | DOI | MR | Zbl

[12] Fulton, William; Pragacz, Piotr Schubert varieties and degeneracy loci, Lecture Notes in Mathematics, 1689, Springer-Verlag, Berlin, 1998, xii+148 pages (Appendix J by the authors in collaboration with I. Ciocan-Fontanine) | DOI | MR | Zbl

[13] Ikeda, Takeshi; Mihalcea, Leonardo C.; Naruse, Hiroshi Double Schubert polynomials for the classical groups, Adv. Math., Volume 226 (2011) no. 1, pp. 840-886 | DOI | MR | Zbl

[14] Kazarian, Maxim On Lagrange and symmetric degeneracy loci (2000) (Isaac Newton Institute for Mathematical Sciences Preprint Series)

[15] Kirillov, Anatol N. Notes on Schubert, Grothendieck and key polynomials, SIGMA Symmetry Integrability Geom. Methods Appl., Volume 12 (2016), Paper no. Paper No. 034, 56 pages | DOI | MR | Zbl

[16] Lambert, Jordan Theta-vexillary signed permutations, Electron. J. Combin., Volume 25 (2018) no. 4, Paper no. Paper 4.53, 30 pages | MR | Zbl

[17] Lascoux, Alain; Schützenberger, Marcel-Paul Polynômes de Schubert, C. R. Acad. Sci. Paris Sér. I Math., Volume 294 (1982) no. 13, pp. 447-450 | MR | Zbl

[18] Lascoux, Alain; Schützenberger, Marcel-Paul Schubert polynomials and the Littlewood–Richardson rule, Lett. Math. Phys., Volume 10 (1985) no. 2-3, pp. 111-124 | DOI | MR | Zbl

[19] West, Julian Generating trees and the Catalan and Schröder numbers, Discrete Math., Volume 146 (1995) no. 1-3, pp. 247-262 | DOI | MR | Zbl

Cited by Sources: