**Instructor:** Igor Pak

pak@math.ucla (add .edu at the end)

**Class schedule:** MWF 2:00 - 2:50 pm, MS 7608

**Office Hours:** M 11-11:50, MS 6125

- Richard Stanley,
*Enumerative Combinatorics*, vol 1 (EC1, second edition), and vol. 2 (EC2).

Download vol 1 from the author's website. - Philippe Flajolet and Robert Sedgewick (FS),
*Analytic Combinatorics*

Download the book here. - Andrew Odlyzko, Asymptotic enumeration methods (AEM), in
*Handbook of Combinatorics*, vol. 2, Elsevier, 1995, pp. 1063-1229.

Download the survey here. - M. Petkovsek, H. S. Wilf and D. Zeilberger,
*A = B*, AK Peters, Wellesley, MA, 1996.

Download the book here.

*Warning*: some of these links require UCLA subscription; whenever possible I tried to include free links.

- H. Wilf, What is an answer?, Monthly article.
- H. Furstenberg, Algebraic functions over finite fields, J. Algebra 7 (1967), 271-277.
- L. Lipshitz, The diagonal of a D-finite power series is D-finite, J. Algebra 113 (1988), no. 2, 373-378.
- I. Gessel, A factorization for formal Laurent series and lattice path enumeration, J. Combin. Theory, Ser. A 28 (1980), no. 3, 321-337.
- P. Flajolet, S. Gerhold and B. Salvy, On the non-holonomic character of logarithms, powers, and the n-th prime function, Electron. J. Combin. 11 (2004/06), A2, 16 pp.
- S. Garoufalidis, G-functions and multisum versus holonomic sequences, Advances Math. 220 (2009), 1945-1955.
- M. Klazar, Bell numbers, their relatives, and algebraic differential equations, J. Combin. Theory, Ser. A 102 (2003), 63–87.
- M. Klazar, Irreducible and connected permutations, Institut teoretické informatiky (ITI) Series, 2003.
- I. Pak, Computation of the Tutte polynomial of complete graphs, preprint (1993).
- R.P. Stanley, A survey of alternating permutations, in
*Contemp. Math*, 2010. - S. Garrabrant and I. Pak, Pattern avoidance is not P-recursive, preprint, 2015.
- S. Garrabrant and I. Pak, Words in linear groups, random walks, automata and P-recursiveness, preprint, 2015.
- C. Banderier and M. Drmota, Formulae and Asymptotics for Coefficients of Algebraic Functions, Combinatorics, Probability and Computing 24 (2015), 1-53.
- M. Kontsevich and D. Zagier, Periods, preprint, 2001.
- N.G. de Bruijn,
*Asymptotic methods in analysis*, Dover, 1981, §4.7. - N.G. de Bruijn, On Mahler's partition problem, Indag. Math. 10, 210–220.
- P van Emde Boas, The Convenience of Tilings, in
*Complexity, logic, and recursion theory*, Dekker, New York, 1997, 331-363. - R.M. Robinson, Periodicity of Somos sequences, Proc. AMS 116 (1992), 613-619.
- J. Propp, The Somos Sequence Site.
- MacMahon Master theorem, Wikipedia page.
- Wilf-Zeilberger pair, Wikipedia page.

Click here to return to Igor Pak Home Page.

*Last updated 12/19/2016*.