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@book{Eis,
	Author = {D. Eisenbud},
	Date-Added = {2018-11-14 17:57:38 +0000},
	Date-Modified = {2018-11-14 18:01:32 +0000},
	Publisher = {Springer},
	Series = {Graduate Texts in Mathematics},
	Title = {Commutative Algebra with a View Toward Algebraic Geometry},
	Year = {1995}}

@book{Sing,
	Author = {G.-M. Greuel and G. Pfister},
	Date-Added = {2018-11-14 17:37:10 +0000},
	Date-Modified = {2018-11-14 17:43:03 +0000},
	Publisher = {Springer},
	Title = {A Singular Introduction to Commutative Algebra},
	Year = {2008}}

@article{A,
	Author = {D. Anderson},
	Date-Added = {2018-11-14 17:34:28 +0000},
	Date-Modified = {2019-05-28 16:35:20 +1000},
	Journal = {Electron. J. Combin.},
	Number = {3},
	Pages = {P3.46, 23 pp},
	Title = {Diagrams and essential sets for signed permutations},
	Url = {https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i3p46},
	Volume = {25},
	Year = {2018}}

@misc{AF12,
	Author = {D. Anderson and W. Fulton},
	Date-Added = {2018-11-14 17:31:41 +0000},
	Date-Modified = {2019-05-28 16:35:35 +1000},
	Eprint = {1210.2066},
	Eprinttype = {arxiv},
	Title = {Degeneracy Loci, Pfaffians, and Vexillary Signed Permutations in Types B, C, and D},
	Year = {2012}}

@misc{AF18,
	Author = {D. Anderson and W. Fulton},
	Date-Added = {2018-11-14 17:31:41 +0000},
	Date-Modified = {2019-05-28 16:35:59 +1000},
	Eprint = {1806.01230},
	Eprinttype = {arxiv},
	Title = {Vexillary signed permutations revisited},
	Year = {2018}}

@article{F92,
	Author = {W. Fulton},
	Date-Added = {2018-11-14 17:26:19 +0000},
	Date-Modified = {2019-05-28 16:38:29 +1000},
	Doi = {10.1215/s0012-7094-92-06516-1},
	Journal = {Duke Math. J.},
	Number = {3},
	Pages = {381-420},
	Title = {Flags, Schubert polynomials, degeneracy loci, and determinantal formulas},
	Volume = {65},
	Year = {1992}}

@book{Mac91,
	Author = {I. G. Macdonald},
	Date-Added = {2018-11-14 17:20:28 +0000},
	Date-Modified = {2019-05-28 16:42:51 +1000},
	Publisher = {Universit{\'e} de Qu{\'e}bec {\`a} Montr{\'e}al, Canada},
	Title = {Notes on Schubert Polynomials},
	Year = {1991}}

@article{LY,
	Author = {L. Li and A. Yong},
	Date-Added = {2018-11-14 17:08:34 +0000},
	Date-Modified = {2019-05-28 16:42:12 +1000},
	Doi = {10.1016/j.aim.2011.09.010},
	Journal = {Adv. Math.},
	Number = {1},
	Pages = {633-667},
	Title = {Some degenerations of Kazhdan--Lusztig ideals and multiplicities of Schubert varieties},
	Volume = {229},
	Year = {2012}}

@article{GR,
	Author = {S. Ghorpade and K. Raghavan},
	Date-Added = {2018-11-14 17:05:50 +0000},
	Date-Modified = {2019-05-28 16:39:58 +1000},
	Doi = {10.1090/s0002-9947-06-04037-2},
	Journal = {Trans. Amer. Math. Soc.},
	Number = {12},
	Pages = {5401-5423},
	Title = {Hilbert functions of points on Schubert varieties in the symplectic Grassmannian},
	Volume = {358},
	Year = {2006}}

@article{KR,
	Author = {V. Kodiyalam and K. Raghavan},
	Date-Added = {2018-11-14 17:05:50 +0000},
	Date-Modified = {2019-05-28 16:41:06 +1000},
	Doi = {10.1016/s0021-8693(03)00518-0},
	Journal = {J. Algebra},
	Number = {1},
	Pages = {28-54},
	Title = {Hilbert functions of points on Schubert varieties in Grassmannians},
	Volume = {270},
	Year = {2003}}

@thesis{K,
	Author = {V. Kreiman},
	Date-Added = {2018-11-14 17:05:50 +0000},
	Date-Modified = {2018-11-14 17:11:42 +0000},
	Institution = {Northeastern University},
	Title = {Monomial Bases and Applications for Richardson and Schubert Varieties in Ordinary and Affine Grassmannians},
	Type = {Ph.D.},
	Year = {2003}}

@inproceedings{KL,
	Author = {V. Kreiman and V. Lakshmibai},
	Booktitle = {Contributions to Automorphic Forms, Geometry, and Number Theory},
	Date-Added = {2018-11-14 17:05:50 +0000},
	Date-Modified = {2019-05-28 16:41:39 +1000},
	Editor = {H.~Hida and D.~Ramakrishnan and F.~Shahidi},
	Pages = {573-597},
	Publisher = {Johns Hopkins University Press, Baltimore, MD},
	Title = {Richardson varieties in the Grassmannian},
	Year = {2004}}

@article{EYD,
	Author = {T. Ikeda and H. Naruse},
	Date-Added = {2018-11-14 16:57:26 +0000},
	Date-Modified = {2019-05-28 16:40:30 +1000},
	Doi = {10.1090/s0002-9947-09-04879-x},
	Journal = {Trans. Amer. Math. Soc.},
	Number = {10},
	Pages = {5193-5221},
	Title = {Excited Young diagrams and equivariant Schubert calculus},
	Volume = {361},
	Year = {2009}}

@article{BLa98,
	Author = {S. Billey and T.~K. Lam},
	Date-Added = {2018-11-14 17:08:34 +0000},
	Date-Modified = {2019-05-28 16:36:48 +1000},
	Doi = {10.1023/a:1008633710118},
	Journal = {J. Algebraic Combin.},
	Number = {2},
	Pages = {139-152},
	Title = {Vexillary elements in the hyperoctahedral group},
	Volume = {8},
	Year = {1998}}

@book{BL,
	Author = {S. Billey and V. Lakshmibai},
	Date-Added = {2018-11-14 16:46:22 +0000},
	Date-Modified = {2019-05-28 16:36:16 +1000},
	Number = {182},
	Publisher = {Birkh{\"a}user},
	Series = {Progress in Mathematics},
	Title = {Singular Loci of Schubert Varieties},
	Year = {2000}}

@article{RZ01,
	Author = {J. Rosenthal and A. Zelevinsky},
	Date-Modified = {2019-05-28 16:43:20 +1000},
	Doi = {10.1023/a:1011253800374},
	Journal = {J. Algebraic Combin.},
	Number = {2},
	Pages = {213-218},
	Title = {Multiplicities of points on Schubert varieties in Grassmannians},
	Volume = {13},
	Year = {2001}}

@article{WY08,
	Author = {A. Woo and A. Yong},
	Date-Modified = {2019-05-28 16:43:52 +1000},
	Doi = {10.1016/j.jalgebra.2007.12.016},
	Journal = {J. Algebra},
	Number = {2},
	Pages = {495-520},
	Title = {Governing singularities of Schubert varieties},
	Volume = {320},
	Year = {2008}}