Home Up Greg Warrington: Research

## Research

 Interests: My interests are algebraic combinatorics (Kazhdan-Lusztig polynomials, combinatorics of Weyl groups, and diagonal harmonics) and gerrymandering PDF format Interactions between geographic clustering and district size In preparation. Gerrymandering and the net number of US House seats won due to vote-distribution asymmetries (also on arXiv) Joint with J. Buzas. Ver. 2 (minor revisions) Submitted. Guest post on Rick Hasen's Election Law Blog. Quantifying gerrymandering using the vote distribution (also on arXiv) To appear, Election Law Journal gzipped tar file of python code used to generate data in ELJ paper Friendly introduction to the declination introduced in above article. The declination is essentially the angle between the two black lines. The bigger the angle, the more partisan asymmetry. Click below to enlarge. Python code to compute the declination. Click the image for animation from 1972 to 2016 Notes on the animation: The cartogram adjusts state sizes according to the number of congressional seats. The sizes used are based on the sizes of the 2012 congressional declinations. The version of the declination used is one (delta tilde) that is essentially independent of the number of seats. The 2003 Texas redistricting is striking. States without at least one seat won by each party are in gray. Sorry Don Young and HI, you didn't fit. Quasisymmetric and Schur expansions of cycle index polynomials Joint with N. Loehr. Submitted. Sage worksheet for computations in the paper. also as a text file Orthogonal bases for transportation polytopes applied to Latin squares, magic squares and Sudoku boards In revision. Sage worksheet for constructing bases described in the paper. Combinatorics of the mirabolic RSK correspondence Joint with J. Godbout Eternally in preparation. Motzkin identities arising in the computation of modified Macdonal polynomials Joint with D. Velleman Eternally in preparation. Sweep maps: A continuous family of sorting algorithms Joint with D. Armstrong and N. Loehr Sage worksheet for checking various conjectures described in the paper. Advances in Mathematics, 284 (2015), 159-85. Rational parking functions and Catalan numbers Joint with D. Armstrong and N. Loehr Sage worksheet for checking various conjectures described in the paper. To appear, Annals of Combinatorics. Shape and pattern containment of separable permutations Joint with A. Crites and G. Panova Ars Combinatoria, to appear. Martin Gardner's minimum no-three-in-a-line problem Joint with A. Cooper, O. Pikhurko and J. Schmitt American Mathematical Monthly, 121:3 (2014), 213-221. Transition matrices for symmetric and quasisymmetric Hall-Littlewood polynomials Joint with N. Loehr and L. Serrano Journal of Combinatorial Theory, Series A, 120:8 (2013), 1996-2019. Sage worksheet for computing various matrices described in the paper. On the existence of three dimensional Room frames and Howell cubes Joint with J. Dinitz and E. Lamken Discrete Math, 313:12 (2013), 1368-1384. Find it here. What to expect from a game of Memory Joint with D. Velleman American Mathematical Monthly, 120:9 (2013), 787-805. Quasisymmetric expansions of Schur-function plethysms Joint with N. Loehr Proceedings of the AMS, 140 (2012), 1159--1171. Equivalence classes for the mu-coefficient of Kazhdan-Lusztig polynomials in S_n Experimental Math., 20 (2011), no. 4, 457--466. The Spectra of Certain Classes of Room Frames: The Last Cases Joint with J. Dinitz Elec. J. Combin. 17 (2010), no. 1, Research Paper 74, 13 pp. From quasisymmetric expansions to Schur expansions via a modified inverse Kostka matrix Joint with E. Egge and N. Loehr European J. Combin. 31 (2010), no. 8, 2014--2027. A combinatorial version of Sylvester's four-point problem Adv. in App. Math., 45 (2010) no. 3, 390--394. A continuous family of partition statistics equidistributed with length Joint with N. Loehr J. Combin. Theory Ser. A 116 (2009), no. 2, 379--403. (final version) Nested quantum Dyck paths and nabla(s_lambda) Joint with N. Loehr International Mathematics Research Notices 2008; Vol 2008: article ID rnm157 (final version) Bitableaux bases for Garsia-Haiman modules of hollow type Joint with E. Allen and M. Cox J. Combin. Theory Ser. A 115 (2008), no. 7, 1127--1155. A human proof for a generalization of Shalosh B. Ekhad's 10^n Lattice Paths Theorem Joint with N. Loehr and B. Sagan Ars Combin. 89 (2008), 421--429. Square q,t-lattice paths and nabla(p_n) Joint with N. Loehr Transactions of the AMS, 359 (2007) no. 2, 649-669. The combinatorics of a three-line circulant determinant Joint with N. Loehr and H. Wilf Israel Journal of Mathematics 143 (2004), 141-156 Juggling probabilities American Mathematical Monthly 112, no. 2 (2005), 105-118 Counterexamples to the 0,1-Conjecture Joint with T. McLarnan Represent. Theory 7 (2003), 181-195 (final version) A formula for inverse Kazhdan-Lusztig polynomials in S_n. J. Comb. Theory A, Vol. 104, Iss. 2 , November (2003), 301-316 (final version) Maximal singular loci for Schubert varieties in SL(n)/B. Joint with S. Billey Trans. AMS 355 (2003), no. 10, 3915--3945 (electronic) (final version) Kazhdan-Lusztig polynomials for 321-hexagon-avoiding permuations. Joint with S. Billey J. of Alg. Comb., 13 (2): 111-136, March 2001 (final version) TBA Joint with Jill Warrington In preparation. TBA Michelle L. Brown, Therese M. Donovan, Ruth M. Mickey, Gregory S. Warrington, W. Scott Schwenk, David M. Theobald In revision. Estimating landscape carrying capacity through maximum clique analysis Joint with Therese M. Donovan, W. Scott Schwenk and Jeffrey H. Dinitz Ecological Applications, 22:8 (2012), 2265-2276. A Photographic Assignment for Abstract Algebra PRIMUS 19 (2009), no. 6, 561-564. The shape of a pool. Eternally in preparation. Juggling Performers + Math = ? Math Horizons, Feb. 2008. Randomized voting and A sketch of randomized voting. In limbo. Here are the overheads for some of the talks I have given: Quasisymmetric expansions of cycle indices UGA AMS Sectional Meeting; Mar. 2016 Rational Catalan numbers and the sweep map UVM-St. Michael's Combinatorics Seminar; Nov. 2014 Rational q-Catalan numbers and q-binomials Halifax AMS Sectional Meeting; Oct. 2014 The Sweep Map CMS Winter Meeting - Ottawa; Dec. 2013 Quasisymmetric expansions of Schur plethysms Holy Cross AMS Sectional Meeting; Apr. 2011 On the mu-coefficient of Kazhdan-Lusztig polynomials Holy Cross AMS Sectional Meeting; Apr. 2011 An infinite family of partition statistics Penn State AMS Sectional Meeting; Oct. 2009 "Statistics" in Combinatorics Invited talk, MathFest Aug. 2009 in Portland, OR A variation on Sylvester's four-point problem Gems of Combinatorics Session, MathFest Aug. 2009 in Portland, OR Combinatorial structures associated to the nabla operator Banff, Sep. 2007 (Jim Haglund, proxy speaker; thanks Jim!) Combinatorial aspects of nabla(s_lambda) given at CRM, Montreal in May 2007. Square q,t-lattice paths and nabla(p_n) given at FPSAC '05 in Taormina, Sicily in June 2005. Overview of Kazhdan-Lusztig Polynomials given at UPenn combinatorics seminar in October 2003. Counterexamples to the 0,1-Conjecture given at the Computational Lie Theory conference at CRM in June 2002. Maximal Singular Loci for Schubert Varieties in SL(n)/B given at FPSAC '01 meeting in Scottsdale, AZ in May 2001. Kazhdan-Lusztig polynomials for 321-hexagon-avoiding permutations given at the Joint Meeting in Washington, DC in January 2000. Here is my doctoral thesis. My thesis advisor was Sara Billey at MIT (now at Univ. Washington). You can check out my mathematical genealogy at The Mathematics Genealogy Project. My cyborg juggling balls. Code for computing type-A Kazhdan-Lusztig polynomials. This is the code accompanying my paper Equivalence classes for the mu-coefficient of Kazhdan-Lusztig polynomials in S_n. Some old code for computing type-A Kazhdan-Lusztig polynomials. From F01 to S03 I was a postdoc at the University of Massachusetts at Amherst. From F03 to S04 I was an NSF postdoctoral fellow at the University of Pennsylvania. From F04 to F08 I was an Assistant Professor at Wake Forest University in Winston-Salem, NC. From S09 to S14 I was an Assistant Professor at the University of Vermont in Burlington, VT. In S14 I was promoted to Associate Professor with tenure (effective F14).