Preprints and Papers Submitted for Publication

• Some Conjectures on the Zeros of Approximates to the Riemann Xi-function and Incomplete Gamma Functions , arXiv:0910.5228
  
  
• A New Recursion in the Theory of Macdonald Polynomials , joint with A. Garsia. PDF
  
  
• On the Monotone Column Pernament Conjecture, joint with M. Visontai. PDF
  

Published Articles in Preprint Form

(Reprints of definitive published versions available upon request)


• Refinements of the Littlewood-Richardson Rule, joint with K. Luoto, S. Mason, and S. Van Willigenburg. Trans. Amer. Math. Soc., to appear. arXiv:0908.3540
  
  
• Quasisymmetric Schur Functions, joint with K. Luoto, S. Mason, and S. Van Willigenburg. J. Combin. Theory Ser. A, to appear. arXiv:0810.2489
  
  
• 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-Schroder 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 Schroder 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.