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The Holonomic Ansatz I. Foundations and Applications to Lattice Path Counting
Doron Zeilberger
Department of Mathematics, Rutgers University (New Brunswick), Hill Center-Busch Campus, 110 Frelinghuysen Rd., Piscataway, NJ 08854-8019, USA
zeilberg@math.rutgers.edu
Annals of Combinatorics 11 (2) p.227-239 June, 2007
AMS Subject Classification: 05A, 33F10
Abstract:
Many combinatorial quantities belong to the holonomic ansatz. For example, sequences enumerating lattice paths. Once this fact is known, many times empirically obtained “conjectures” can be easily proved automatically.
Keywords: computer-generated combinatorics, lattice path enumeration

References:

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[CaW] E.W.Weisstein et al., Ansatz, from MathWorld ―A Wolfram Web Resource, http://mathworld.wolfram.com/Ansatz.html. [contributed by Mark. D. Carrara]

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[Z1] D. Zeilberger, The holonomic ansatz II: Automatic DISCOVERY(!) and PROOF(!!) of Holonomic Determinant Evaluations, in preparation.

[Z2] D. Zeilberger, The holonomic ansatz III: automatic proofs of positivity theorems for powerseries coefficients of rational functions of several variables, in preparation.

[Z3] D. Zeilberger, The joy of brute force: the covariance of the number of inversions and the major index, Personal Journal of Ekhad and and Zeilbeger, http://www.math.rutgers.edu/~zeilberg/pj.html.

[Z4] D. Zeilberger, A Holonomic systems approach to special functions identities, J. Comput. Appl. Math. 32 (1990) 321-368.

[Z5] D. Zeilberger, Theorems for a price: tomorrow's semi-rigorous mathematical culture, Notices of the American Mathematical Society, 40 (8) (1993) 978-981; reprinted in The Mathematical Intelligencer, 16 (4) (1994) 11-14.