Constitutes the proceedings of a conference that was intended to honour the influence and achievements of Herbert S Wilf who has authored several classical textbooks and research monographs pertaining to the conference themes, namely Combinatorics, Number Theory, and Computer Algebra.

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.​

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.