NSF Proposal: Automated Enumerative Combinatorics

Automated Enumerative Combinatorics

Doron Zeilberger

Department of Mathematics, Rutgers University (New Brunswick), Hill Center-Busch Campus, 110 Frelinghuysen Rd., Piscataway, NJ 08854-8019. zeilberg@math.rutgers.edu

http://www.math.rutgers.edu/~zeilberg/ .

References Cited

[ABKS] J Ablinger, J Blümlein, S Klein, and C Schneider Modern Summation Methods and the Computation of 2- and 3-loop Feynman Diagrams, Nuclear Physics B - Proceedings Supplements 205-206 (2010), 110-115.

http://arxiv.org/pdf/1006.4797 .

[Al] Gert Almkvist, Calabi-Yau differential equations of degree 2 and 3 and Yifan Yang’s pullback, preprint.

http://arxiv.org/abs/math/0612215 .

[AZ] Moa Apagodu and Doron Zeilberger, Multi-Variable Zeilberger and Almkvist-Zeilberger Algorithms and the Sharpening of Wilf-Zeilberger Theory, Adv. Appl. Math. 37(2006), (Special issue in honor of Amitai Regev), 139-152.

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/multiZ.html .

[BZ] Andrew Baxter and Doron Zeilberger, The Number of Inversions and the Major Index of Permutations are Asymptotically Joint-Independently Normal (Second Edition!), Personal Journal of Shalosh B. Ekhad and Doron Zeilberger (refereed by a group of eight world-class experts!), Feb. 4, 2011.

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/invmaj.html .

[BeP] J. Bétréma and J.-G. Penaud, Modèles avec particules dures, animaux dirigé et séries en variables partiellement commutatives .

http://fr.arxiv.org/abs/math/0106210 .

[Bo1] Miklós Bóna, “Combinatorics of Permutations”, Chapman and Hall/CRC, 2004.

[Bo2] Miklós Bóna, Exact enumeration of 1342-avoiding permutations: a close link with labeled trees and planar maps, Journal of Combinatorial Theory, Series A 80 (1997), 257-272.

[BB] J. Borwein and D. Bailey, Mathematics by Experiment. A.K. Peters, Natick, 2004.

[BBCGLM] D. Bailey, J. Borwein, N. Calkin, R. Gingensohn, D. Luke, and V. Moll, ”Experimental Mathematics in Action”, A.K. Peters, 2007.

[EGZ] Shalosh B. Ekhad, Evangelos Georgiadis and Doron Zeilberger, How to Gamble If You’re In a Hurry, Journal of Difference Equations and Application, 19 (2013) , 520-526.

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/himurim.html .

[Gal] J. Gallian, Interview with Doron Zeilberger, MAA Focus May/June 2007, 14-17. (Available

on-line at www.maa.org).

[Gar] Stavros Garoufalidis, On the characteristic and deformation varieties of a knot, Geometry and Topology 7 (2004), 291-309.

http://arxiv.org/pdf/math.GT/0306230 .

[GL] Stavros Garoufalidis and T.T.Q. Le, The colored Jones function is q-holonomic, Geometry and Topology 9 (2005), 1253-1293.

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Doron Zeilberger

http://arxiv.org/pdf/math/0309214 .

[Ge] Ira M. Gessel (1990), Symmetric functions and P-recursiveness, Journal of Combinatorial Theory, Series A 53 (1990), 257-285.

http://people.brandeis.edu/~ssel/homepage/papers/dfin.pdf .

[GZ] Edinah K. Gnang and Doron Zeilberger, Zeroless Arithmetic: Representing Integers ONLY using, to appear in J. Difference Equations and Applications.

http://math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/arif.html .

[Gu] Jesús Guillera, A new Ramanujan-like series for 1/π^{2}, Ramanujan J. 26(2011), 369 - 374.

http://arxiv.org/abs/1003.1915 .

[GR] Jesús Guillera and Mat Rogers, Mahler measure and the WZ-algorithm, Proc. of the Amer. Math. Soc., to appear.

http://arxiv.org/abs/1006.1654 .

[HNTT] Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura, Holonomic gradient method for the distribution function of the largest root of a Wishart matrix, Journal of Multivariate Analysis 117(2013), 296-312.

http://arxiv.org/abs/1201.0472 .

[HZ] Emilie Hogan and Doron Zeilberger, A New Algorithm for Proving Global Asymptotic Stability of Rational Difference Equations, Journal of Difference Equations and Applications 18(2012), 1853-1873.

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/gas.html .

[KKZ] Christoph Koutschan, Manuel Kauers, and Doron Zeilberger, A Proof Of George Andrews’ and David Robbins’ q-TSPP Conjecture, Proceedings of the National Academy of Science, 108 #6 (Feb. 8, 2011), 2196-2199.

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/qtsppRig.html .

[KT] Christoph Koutschan and Thotsaporn Thanatipanonda, Advanced Computer Algebra for Determinants, Annals of Combinatorics, to appear.

http://arxiv.org/abs/1112.0647 .

[K1] C. Krattenthaler, Advanced Determinant Calculus, Sém. Lothar. Comb. 42 (1999), B42q. (“The Andrews Festschrift”, D. Foata and G.-N. Han(eds.)).

http://arxiv.org/abs/math/9902004

[K2] C. Krattenthaler, Advanced Determinant Calculus: A Complement, Linear Algebra Appl. 411(2005), 68-166.

http://arXiv.org/abs/math.Co/0503507 .

[NZ] Brian Nakamura and Doron Zeilberger, Using Noonan-Zeilberger Functional Equations to Enumerate (in Polynomial Time!) Generalized Wilf Classes, Advances in Applied Mathematics 50 (2013), 356-366.

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/Gwilf.html .

[O] Soichi Okada, On the generating functions for certain classes of plane partitions, J. Comb. Theory Ser. A 53(1989), 1-23.

[PWZ] Marko Petkovsek, Herbert Wilf, and Doron Zeilberger, “A=B”, AK Peters, Wellesley,

(1996). Web Page:  http://central.cis.upenn.edu/~wilf/AeqB.html .

[R] John Riordan, “Introduction to Combinatorial Analysis”, John Wiley, 1958. Reprinted by Dover, 2002.

C – 2 [SZ] Andrew V. Sills and Doron Zeilberger, Rademacher’s Infinite Partial Fraction Conjecture is (almost certainly) False, Journal of Difference Equations and Applications 19 (2013), 680-689.

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/hans.html .

[St] Richard Stanley, A baker’s dozen of conjectures concerning plane partitions. In “Combinatoire énumérative”, ed. G. Labelle and P. Leroux. Lecture Notes in Mathematics 1234 (1986), 285-293. Springer Verlag, New York.

http://www-math.mit.edu/~rstan/pubs/pubfiles/67.pdf .

[Su] Zhi-Wei Sun, Super congruences and Euler numbers, China Mathematics 54 (2011), 2509-2535.

http://arxiv.org/abs/1001.4453 .

[T] Marko Thiel, The inversion number and the major index are asymptotically jointly normally distributed on words, preprint.

http://arxiv.org/abs/1302.6708 .

[WZ] Herbert S. Wilf and Doron Zeilberger, An algorithmic proof theory for hypergeometric (ordinary and “q”) multisum/integral identities, Invent. Math. 108(1992), 575-633.

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/multiwz.html .

[V] Vince Vatter, Enumeration schemes for restricted permutations, Combinatorics, Probability and Computing 17(2008), 137-159.

http://www-groups.mcs.st-andrews.ac.uk/~vince/publications/wilfplus/ .

[Z1] Doron Zeilberger, The HOLONOMIC ANSATZ I. Foundations and Applications to Lattice Path Counting, Annals of Combinatorics 11(2007), 227-239 .

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/ansatzI.html .

[Z2] Doron Zeilberger, The HOLONOMIC ANSATZ II. Automatic DISCOVERY(!) and PROOF(!!) of Holonomic Determinant Evaluations, Annals of Combinatorics 11(2007), 241-247 .

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/ansatzII.html .

[Z3] Doron Zeilberger, An Enquiry Concerning Human (and Computer!) [Mathematical] Understanding, in: C.S. Calude, ed., “Randomness & Complexity, from Leibniz to Chaitin”, World Scientific, Singapore, Oct. 2007.

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/enquiry.html .

[Z4] Doron Zeilberger, Teaching the Computer how to Discover(!) and then Prove(!!) (all by Itself(!!!)) Analogs of Collatz’s Notorious 3x+1 Conjecture, J. of Difference Equations and Applications 17(2011), 375-386.

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/collatz.html .

[Z5] Doron Zeilberger, The Amazing 3^{n} Theorem and its even more Amazing Proof [Discovered by Xavier G. Viennot and his École Bordelaise gang], Personal Journal of Shalosh B. Ekhad and Doron Zeilberger, Aug 10, 2012.

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/bordelaise.html .

[Z6] Doron Zeilberger, Enumeration Schemes, and More Importantly, Their Automatic Generation, Annals of Combinatorics 2(1998), 185-195 .

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/wilf.html .

[Z7] Doron Zeilberger, On Vince Vatter’s Brilliant Extension of Doron Zeilberger’s Enumeration Schemes for Counting Herb Wilf’s Classes, Personal Journal of Shalosh B. Ekhad and Doron Zeilberger, Dec. 29, 2006.

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/vatter.html .

[Z8] Doron Zeilberger, Automated Counting of Towers Á La Bordelaise [Or: Footnote to p. 81 of

C – 3 the Flajolet-Sedgewick Chef-d’oeuvre], Personal Journal of Shalosh B. Ekhad and Doron Zeilberger, Dec. 17, 2012 .

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/migdal.html .

[Z9] Doron Zeilberger, The Automatic Central Limit Theorems Generator (and Much More!), Advances in Combinatorial Mathematics: Proceedings of the Waterloo Workshop in Computer Algebra 2008 in honor of Georgy P. Egorychev”, chapter 8, pp. 165-174, (I.Kotsireas, E.Zima, eds. Springer Verlag, 2009) .

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/georgy.html .

[Zu] Wadim Zudilin, Ramanujan-type supercongruences, Journal of Number Theory 129(2009), 18481857.

http://arxiv.org/pdf/0805.2788 .

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