Sara Billey's Publications and Preprints
Check the Mathematics ArXiv and the Computer Science ArXiv!
- Brewing Fubini-Bruhat Orders (with Stark Ryan).
Accepted as a poster for FPSAC 2024. Full length version in progress.
FPSAC Abstract - Cyclotomic Generating functions (with Josh Swanson).
Submitted, 2023.
ArXiv - Criteria for smoothness of positroid varieties via
pattern avoidance, Johnson graphs, and spirographs (with Jordan
Weaver and appendix by Christian Krattenthaler). Accepted as a talk
for FPSAC 2022 Bangalore. To appear Trans. AMS.
ArXiv FPSAC Abstract Recorded Lecture from FPSAC July 22, 2022. - The moduli space of limit laws for q-hook formulas (with
Joshua Swanson). Combinatorial Theory, Volume 2, Issue 2 (2022).
ArXiv Journal Article Recorded Lecture from University Kentucky's Combinatoircs Seminar on November 2, 2020. - Existence and hardness of conveyor belts
(with Molly Baird, Erik Demaine, Martin Demaine, David
Eppstein, Sandor Fekete, Graham Gordon, Sean Griffin, Joseph
S. B. Mitchell, Joshua P. Swanson). Electroinc Journal of
Combinatorics, 27(4). Paper No. 4.25.
ArXiv Journal Article -
Tableaux posets and the fake degrees of coinvariant algebras
(with Matjaz Konvalinka and Joshua Swanson). Advances in
Math, Volume 371, 16 September 2020, 107252.
ArXiv Journal Article - Pop-stack sorting and its image: Permutations with
overlapping runs (with Andrei Asinowski, Cyril Banderier, Benjamin
Hackl, and Svante Linusson). Acta Mathematica Universitatis
Comenianae, Proceedings of Eurocomb 2019 (Bratislava, Slovakia 26-30
August, 2019), vol. 88, no.3.
Eurocomb Proceedings - Boolean product polynomials, Schur positivity, and Chern
plethysm (with Brendon Rhoades and Vasu Tewari). IMRN 2019.
ArXiv Journal Article -
Boolean product polynomials and Schur-positivity
(with Louis Billera and Vasu Tewari) Accepted as a Talk
at FPSAC 2018.
Séminaire Lotharingien de Combinatoire - FPSAC 2018
Issue 80B
Proceedings of the 30th International Conference on "Formal Power Series and Algebraic Combinatorics", July 16 - 20, 2018, Dartmouth College, Hanover, USA
ArXiv FPSAC Abstract -
A bijective proof of Macondald's Reduced Word Formula
with Ben Young and Alexander Holroyd. Accepted to
FPSAC 2016 as a talk. Published in Algebraic Combinatorics, Volume 2 (2019) no. 2, pp. 217-248.
ArXiv FPSAC 2016 Journal Article -
Parabolic Double Cosets in Coxeter Groups
(with Matjaz Konvalinka, T.Kyle Petersen, William Slofstra, and Bridget
Tenner). Accepted to FPSAC 2016 as a poster. Electronic Journal of
Combinatorics, Volume 25, Issue 1 (2018), Article P1.23.
ArXiv FPSAC 2016 Journal Article - On the enumeration of tanglegrams and tangled chains
with Matjaz Konvalinka, Frederick A Matsen IV. Journal of
Combinatorial Theory, Series A Volume 146, February 2017, Pages
239-263.
ArXiv FPSAC 2016 Journal Article - The Contributions of Stanley to the Fabric of Symmetric and Quasisymmetric Functions with Peter McNamara, posted May 2015. Appeared in The Mathematical Legacy of Richard P. Stanley Edited by Patricia Hersh, Thomas Lam, Pavlo Pylyavskyy, and Victor Reiner. Published by the AMS, 2016.
- Coefficients and Roots of Peak Polynomials with Matthew Fahrbach and Alan Talmage. Experimental Math, Volume 25, 2016 - Issue 2, 2015. Additional data for Peak Polynomials and their complex zeros.
- Coxeter-Knuth graphs and a signed Little map for type B reduced words with Zachary Hamaker, Austin Roberts, and Benjamin Young. Electronic Journal of Combinatorics, v. 21, issue 4 (2014), paper P4.6
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Consequences of the Lakshmibai-Sandhya Theorem: the ubiquity of permutation patterns in Schubert calculus and related geometry
with Hiraku Abe. Schubert calculus—Osaka 2012, 1–52,
Adv. Stud. Pure Math., 71, Math. Soc. Japan, [Tokyo], 2016.
ArXiv Recorded Lectures from Schubert Calculus—Osaka 2012. Journal Article - On meteors, earthworms and WIMPs with Krzysztof Burdzy, Soumik Pal, and Bruce Sagan. Annals of Probability, vol . 25, num.4. 2015.
- Permutation Patterns, Stanley Symmetric Functions and Generalized Specht Modules with Brendan Pawlowski. Preprint. To appear in J. Combinatorial Theory Series A. Extended abstract accepted as a talk at FPSAC 2013. Associated pattern data.
- Fingerprint Databases for Theorems with Bridget Tenner. Notices of the AMS, Sept. 2013.
- Permutations With Given Peak Set with Krzystof Burdzy and Bruce Sagan. J. Integer Sequences, Vol. 16 (2013).
- Affine dual equivalence and k-Schur functions. with Sami Assaf. Journal of Combinatorics, special issue in honor of Adriano Garsia. Vol 3, Num 3, p. 343-399, 2012
- Pattern characterization of rationally smooth affine Schubert varieties of type A. with Andrew Crites. Journal of Algebra, Volume 361, 1 July 2012, Pages 107-133.
- Singularities of generalized Richardson varieties with Izzet Coskun. Communications in Algebra, Volume 40, Issue 4, April 2012, pages 1466-1495.
- REU Report on Branched Polymers with Tom Boothby, Chris Fox and Morgan Eichwald. Manuscript. See also Polymer code in SAGE
- Smooth and palindromic Schubert varieties in affine Grassmannians. with Steve Mitchell. Journal of Algebraic Combinatorics (2010) 31:169-216.
- Permutations with Kazhdan-Lusztig polynomial P_{id,w}(q) = 1 + q^h by Alex Woo, with an appendex by myself and Jonathan Weed. The Electronic Journal of Combinatorics Volume 16(2), 2009. Published May 12, 2009.
- Affine partitions and affine Grassmannians with Steve Mitchell. Electronic Journal of Combinatorics, Special Issue in honor of Anders Bjorner's 60th Birthday, R18, Volume 16(2), 2009. Computer code in lisp and Maple
- Embedded factor patterns for Deodhar elements in Kazhdan-Lusztig theory with Brant Jones to appear in the Special Issue of Annals of Combinatorics dedicated to Permutation Patterns, 2008.
- Flag arrangements and triangulations of products of simplicies with Federico Ardila. Advances in Math. 214 (2007), no. 2, 495--524. 32S22 (14M15).
- Intersections of Schubert varieties and other permutation array schemes with Ravi Vakil. IMA Volumes in Mathematics and its Applications Volume 146: Algorithms in Algebraic Geometry, 2007, pages 21--54. Code for experimentation is available here.
- Smoothness of Schubert Varieties via Patterns in Root Systems . Joint with Alex Postnikov. Advances in Applied Math v. 34 (2005) p. 447-466.
- A vector partition function for the multiplicities of sl_k(C). Joint with Etienne Rassart and Victor Guillemin. Journal of Algebra, vol. 278 (2004) no. 1, 251-293.
- Lower bounds for Kazhdan-Lusztig polynomials from patterns . Joint with Tom Braden. Transform. Groups vol. 8 (2003) no. 4, 321-332.
- Maximal Singular Loci of Schubert Varieties in SLn/B (with Gregory Warrington) in Trans. AMS. 355 (2003), no. 10, 3915-3945.
- Kazhdan-Lusztig Polynomials for 321-hexagon-avoiding permutations, (with Gregory Warrington) in J. of Algebraic Combinatorics, v. 13 (2001), no. 2, 111--136.
- The Parabolic map. (joint with Ken Fan and Jozsef Losonczy) J. of Alebra, vol. 214 (1999).
- Kostant Polynomials and the Cohomology Ring for G/B. Duke Journal of Math, Volume 96, No. 1, pp. 205-224, 1999. This is the extended version of the announcement that appeared in the Proceedings of the National Academy of Science.
- Kostant Polynomials and the Cohomology Ring for G/B Proceedings of the National Academy of Science, Jan.1997.
- Pattern Avoidance and Rational Smoothness of Schubert varieties. Advances in Math, vol. 139 (1998) pp. 141--156.
- Vexillary elements of the hyperoctahedral group Sara Billey and Tao Kai Lam. J. of Algebraic Combinatorics, v.8 (1998) pp. 139-152. Lisp code is available upon request for verifying the computer aided proof in this paper.
- Transition Equations for Isotropic Flag Manifolds. Discrete Math., Special Issue devoted to the Conference in Taormina, Sicilly, in honor of Adriano Garsia, vol. 193 (1998) pp. 69--84.
- Schubert Polynomials for the classical groups , Sara Billey and Mark Haiman Journal of AMS Volume 8, Number 2, April 1995
- RC-Graphs and Schubert polynomials Nantel Bergeron and Sara Billey Experimental Mathematics, Vol.2 (1993), No. 4. Errata with 2 corrections.
- Some Combinatorial Properties of Schubert Polynomials , Sara Billey, Richard Stanley, and William Jockusch J. of Algebraic Comb. Vol. 2 Num. 4, 1993.
- An Abstract Definition of Schubert Polynomials. University of California, San Diego, Ph.D. thesis 1994. Available upon request.