Advances in Combinatorics : Waterloo Workshop in Computer Algebra W80 May 26 29 2011 This volume as Andrew M. Odlzyko writes in the foreword “commemorates and celebrates the life and achievements of an extraordinary person.” Originally conceived as an 80th birthday tribute to Herbert Wilf the well known combinatorialist the book has evolved beyond the proceeds of the W80 tribute. Professor Wilf was an award winning teacher who was supportive of women mathematicians and who had an unusually high proportion of women among his PhD candidates. He was Editor in chief of the American Mathematical Monthly and a founder of both the Journal of Algorithms and of the Electronic Journal of Combinatorics. But he was first a researcher driven by his desire to know and explain the inner workings of the mathematical world. The book collects high quality refereed research contributions by some of Professor Wilf’s colleagues students and collaborators. Many of the papers presented here were featured in the Third Waterloo Workshop on Computer Algebra (WWCA 2011 W80) held May 26 29 2011 at Wilfrid Laurier University Waterloo Canada. Others were included because of their relationship to his important work in combinatorics. All are presented as a tribute to Herb Wilf’s contributions to mathematics and mathematical life. Foreword by Andrew M. Odlyzko Glaisher’s formulas for 1 p2 and some generalizations: Gert Almkvist Complementary Bell numbers: Arithmetical properties and Wilf’s conjecture: Tewodros Amdeberhan and Valerio De Angelis and Victor H. Moll. Partitions With Early Conditions: George E. Andrews Hypergeometric identities associated with statistics on words: George E. Andrews Carla D. Savage and Herbert S. Wilf Stationary Distribution and Eigenvalues for a de Bruijn Process: Arvind Ayyer and Volker Strehl Automatic Generation of Theorems and Proofs on Enumerating Consecutive Wilf Classes: Andrew Baxter Brian Nakamura and Doron Zeilberger Watson–Like Formulae for Terminating 3F2 Series: Wenchang Chu and Roberta R. Zhou Balls in Boxes: Variations on a Theme of Warren Ewens and Herbert Wilf: Shalosh B. Ekhad and Doron Zeilberger Beating Your Fractional Beatty Game Opponent and: What’s the Question to Your Answer Aviezri S. Fraenkel WZ proofs of “divergent” Ramanujan type series: Jesús Guillera Smallest parts in compositions: Arnold Knopfmacher and Augustine O. Munagi Cyclic Sieving for Generalised Non Crossing Partitions Associated with Complex Reflection Groups of Exceptional Type: Christian Krattenthaler and ThomasW. M¨ uller Set partitions with no m nesting: Marni Mishna and Lily Yen The distribution of zeros of the derivative of a random polynomial: Robin Pemantle and Igor Rivin On the distribution of small denominators in the Farey series of order N: C.L. Stewart Lost in translation: Wadim Zudilin.