Combinatorics of Integer Sequences (Math 206, Fall 2016)

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

Main Reading Sources:

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.

Selected additional reading:

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.

Course Notes:

The (unchecked) notes are taken by Bon-Soon Lin and are available in one file (in two-page .pdf).

Click here to return to Igor Pak Home Page.

Last updated 12/19/2016.