Preprints and Papers Submitted for Publication
- Bosonic-Fermionic Diagonal Coinvariants and Theta Operators ,
joint with Francois Bergeron, Alessandro Iraci and Marino Romero.
Submitted to Conference Proceedings of the Open Problems in Algebraic Combinatorics (OPAC)
Conference, held at the Univ. of Minnesota in May, 2022.
pdf
- The Super Nabla Operator,
joint with Francois Bergeron, Alessandro Iraci and Marino Romero.
arXiv:2303.00560
- e-Positivity Results and Conjectures,
joint with Adriano Garsia, Dun Qiu, and Marino Romero.
arXiv:1904.07912
Published Articles in Preprint Form
- Combinatorial Formulas for (Type A) Macdonald Polynomials,
Contemporary Mathematics Volume on "Macdonald Theory and Beyond:
Combinatorics, Geometry and Integrable Systems", an AMS Special Session held online in March 2022, to appear.
pdf
- Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials,
joint with Sylvie Corteel, Sarah Mason, Olya Mandelshtam and Lauren Williams.
arXiv:2004.11907
Selecta Mathematica, 28 (2022), Paper No. 32, 33 pages.
(Link to the extended abtsract in the proceedings of the FPSAC 2020 conference:
arXiv:1912.03390)
- Schedules and the Delta Conjecture,
joint with Emily Sergel.
arXiv:1908.04732
Ann. of Combin., 25 (2021), pp. 1-31.
- Macdonald polynomials and chromatic quasisymmetric functions,
joint with Andy Wilson.
arXiv:1701.05622
Elec. J. Combin., 27 (2020), Paper No. 3.37, 21 pages.
- Some conjectures on the Schur expansion of Jack polynomials,
joint with Per Alexandersson and George Wang.
J. of Combin., 12 (2021), 215--233.
pdf
(Link to extended abstract appearing in the FPSAC 2018 Proceedings),
arXiv:1805.00511
- Combinatorial aspects of Macdonald and related polynomials,
Encyclopedia of Special Functions: The Askey-Bateman Project, Chapter 10 in Volume 2 on Multivariable Special Functions,
T. Koornwinder and J. Stokman, editors,
Cambridge University Press, ISBN 9781107003736, (2020).
PDF
- Real-rootedness of variations of Eulerian polynomials,
joint with Philip Zhang. Adv. in Appl. Math., 109 (2019), 38-54.
arXiv:1902.01278
- A proof of the Delta Conjecture when q=0,
joint with Adriano Garsia, Jeff Remmel, and Meesue Yoo. Ann. of Combin., 23 (2019), 317-333.
arXiv:1710.07078
- Some new symmetric function tools and their applications,
joint with Adriano Garsia and Marino Romero. J. of Combin. (special issue in honor of Jeff Remmel),
10 (2019), 655-674.
pdf
- p-Rook numbers and cycle counting in Cp wreath Sn,
joint with Jeff Remmel and Messue Yoo.
Developments in Mathematics, Vol. 58, Lattice Path Combinatorics and its Appl., Andrews, G. E., Krattenthaler, C., Krinik, A. (Eds.),
Springer (2019), pp. 250-282.
PDF
- Hall-Littlewood expansions of Schur Delta operators at t=0,
joint with Brendon Rhoades and Mark Shimozono.
Seminaire Lotharingien, B79c (2019), 20pp.
pdf
- A generalized major index statistic on tableaux,
joint with Emily Sergel. Seminaire Lotharingien, B78b (2018), 8 pp.
pdf
- Ordered set partitions, generalized coinvariant algebras, and the Delta Conjecture,
joint with Brendon Rhoades and Mark Shimozono. Adv. Math., 19 (2018), 851-915.
arXiv:1609.07575
- The Delta conjecture,
joint with Jeff Remmel and Andy Wilson. Trans. Amer. Math. Soc., 370 (2018), 4029-4057.
arXiv:1509.07058
- Some new applications of the Stanley-Macdonald Pieri Rules
,
joint with Adriano Garsia, Guoce Xin, and Mike Zabrocki.
The Mathematical Legacy of Richard Stanley, AMS, Providence, RI, Hersh, P., Lam, T., Pylyavskyy, P.,
Reiner, V. (Eds.), 2016, pp. 141-168.
arXiv:1407.7916
- The combinatorics of knot invariants arising from the study of Macdonald polynomials,
Recent Trends in Combinatorics, The IMA
Volumes in Math. and its Applications, Vol. 159, Beveridge, A., Griggs, J.R., Hogben, L.,
Musiker, G., Tetali, P. (Eds.), 2016, pp. 579-600.
PDF.
- Catalan Paths and q,t-Enumeration,
Handbook of Enumerative Combinatorics, Discrete Math. Appl. (Boca Raton), CRC Press (2015), 679-751.
PDF
- A polynomial expression for the character of diagonal harmonics,
joint with A. Garsia. Ann. Combin., 19 (2015), 693-703.
PDF
- Constant term methods in the theory of Tesler matrices and Macdonald polynomial operators,
joint with A. Garsia and G. Xin. Ann. Combin., 18 (2014), 83-109.
PDF
- Properties of the nonsymmetric Robinson-Schensted-Knuth algorithm,
joint with Sarah Mason and Jeff Remmel. J. Algebraic Combin., 38 (2013), 285-327.
PDF
- Combinatorics of Tesler matrices in the theory of parking functions and diagonal harmonics,
joint with D. Armstrong, A. Garsia, B. Rhoades, and B. Sagan. J. Comb., 3 (2012), 451-494.
PDF
- Stable multivariate Eulerian polynomials and generalized Stirling permutations,
joint with M. Visontai. Eur. J. Combin., 33 (2012), 477-487.
PDF
- A new recursion in the theory of Macdonald polynomials,
joint with A. Garsia. Ann. Combin., 16 (2012), 77-106.
PDF
- A compositional shuffle conjecture specifying touch points of the Dyck path,
joint with Jennifer Morse and Mike Zabrocki. Canad. J. Math., 64 (2012), 822-844.
arXiv:1008.0828
- Proof of the monotone column permanent conjecture,
joint with P. Brändén, M. Visontai and D. G. Wagner.
in: P. Brändén, M. Passare, M. Putinar (Eds.), Notions of positivity and the geometry of polynomials
(Trends in Mathematics), Birkhäuser, Basel (2011), 63-78.
arXiv:1010.2565
- A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants,
Adv. Math., 227 (2011), 2092-2106. PDF
- Some conjectures on the zeros of approximates to the Riemann Xi-function and incomplete
gamma functions,
Cent. Eur. J. Math., 9(2) (2011), 302-318.
PDF
- Refinements of the Littlewood-Richardson rule,
joint with K. Luoto, S. Mason, and S. Van Willigenburg.
Trans. Amer. Math. Soc., 363 (2011), 1665-1686.
arXiv:0908.3540
- Quasisymmetric Schur functions,
joint with K. Luoto, S. Mason, and S. Van Willigenburg.
J. Combin. Theory Ser. A, 118 (2011), pp. 463-490.
arXiv:0810.2489
- On the Monotone Column Permanent conjecture,
joint with M. Visontai. Discrete Math. Theor. Comput. Sci., Proceedings of the FPSAC 2009
conference, volume (2009), pp 443-454.
PDF
- A combinatorial formula for non-symmetric Macdonald polynomials,
joint with M. Haiman and N. Loehr.
Amer. J. of Math., 103 (2008), pp. 359-383.
arXiv.org/abs/math.CO/0601693
- An extension of the Foata map to Standard Young Tableaux,
joint with L. Stevens.
Seminaire Lotharingien, 56 (2006), Article B56C.
PDF
- The genesis of the Macdonald polynomial statistics,
Seminaire Lotharingien
(Proceedings of the Garsiafest/Formal Power Series and Algebraic
Combinatorics 2005 conference held in Taormina, Sicily), Vol. 54A.
http://www.mat.univie.ac.at/~slc/
- A combinatorial formula for Macdonald polynomials, joint
with M. Haiman and N. Loehr. Jour. Amer. Math. Soc., 18 (2005), pp. 735-761.
arXiv.org/abs/math.CO/0409538
- A conjectured combinatorial formula for
the Hilbert series for diagonal harmonics, joint with Nick Loehr.
Discrete Math.
(Proceedings of FPSAC 2002 conference held in Melbourne, Australia.)
298 (2005), pp. 189-204.
Postscript ,
PDF
- Combinatorial theory of
Macdonald polynomials I: Proof of Haglund's formula
joint with M. Haiman and N. Loehr.
Proc. Nat. Acad. Sci. USA, 102, No. 8
(2005), pp. 2690-2696.
(Condensed version of the paper "A Combinatorial formula for Macdonald
polynomials").
Article,
Cover Image.
- A combinatorial formula for the character of the diagonal coinvariants,
(31 pages), joint with M. Haiman, N. Loehr, J. Remmel and A. Ulyanov.
Duke Math. J., 126 (2005), pp. 195-232.
arXiv:math.CO/0310424.
- Statistics on wreath products, perfect matchings and signed words, (49 pages), joint with N. Loehr and J. Remmel.
Eur. J. Combin.(special issue on "Combinatorics and Representation
Theory"), 26 (2005), pp. 835-868.
Postscript ,
PDF.
- A combinatorial model for the Macdonald polynomials,
Proc. Nat. Acad. Sci. USA, 101 (2004), pp. 16127-16131.
Postscript ,
PDF
- A proof of the q,t-Schröder conjecture,
Internat. Math. Res. Notices, 11 (2004), pp. 525-560.
Postscript ,
PDF.
- Cycles and perfect matchings, joint with Jeff Remmel.
Discrete Math., 274 (2004), pp. 93-108.
Postscript ,
PDF.
- A Schröder generalization of Haglund's statistic on Catalan paths,
joint with Eric Egge, Darla Kremer and Kendra Killpatrick.
Electron. J. of Combin., 10 (2003), Research Paper 16, 21 pages
(electronic).
Postscript ,
PDF,
- Conjectured statistics for the (q,t)-Catalan numbers,
Adv. Math., 175 (2003), 319-334
Postscript ,
PDF.
- A proof of the q,t-Catalan positivity conjecture,
joint with
Adriano Garsia. LACIM 2000 conference on Combinatorics,
Computer Science and Applications (Montreal, QC),
Discrete Math., 256 (2002), 677-717.
PDF.
- Rook theory for perfect matchings, joint with Jeff Remmel.
Adv. in Appl. Math.,
(Special issue dedicated to D. Foata) 27 (2001), 438-481.
Postscript ,
PDF,
- A positivity result in the theory of Macdonald polynomials,
joint with Adriano Garsia.
Proc. Nat. Acad. Sci. USA, 98
(2001), 4313-4316 (electronic).
Postscript ,
PDF,
-
Further investigations involving
rook polynomials with only real zeros,
Eur. J. Combin., 21 (2000), 1017-1037.
Postscript ,
PDF,
-
Generalized rook polynomials, joint with Jay Goldman.
J. Combin. Theory Ser. A, 91 (2000),
509-530.
Postscript ,
PDF,
- Theorems and conjectures involving rook polynomials with
only real zeros, joint with Ken Ono and David Wagner.
Topics in Number Theory (University Park, PA, 1997),
Math. Appl., 467, Kluwer (1999), 207-221.
Postscript ,
PDF,
- On the nonnegativity of
the coefficients of some polynomials occurring in the
theory of cubical spheres,
Ann. Sci. Math. Quebec, 22 (1998), 43-45.
Postscript ,
PDF,
- q-Rook polynomials and matrices over finite fields,
Adv. in Appl. Math., 20 (1998), 450-487.
Postscript ,
PDF.
- Rook theory and t-cores, joint with Lawrence Sze and Ken Ono.
J. Combin. Theory Ser. A, 84
(1998), 9-37.
Postscript ,
PDF.
- Rook theory and hypergeometric series,
Adv. in Appl. Math., 17 (1996), 408-459.
- Rook theory, compositions and zeta functions,
Trans. Amer. Math. Soc., 348 (1996), 3799-3825.