Connections in Discrete Mathematics

Steve Butler is Associate Professor of Mathematics at Iowa State University. His research interests include spectral graph theory, enumerative combinatorics, mathematics of juggling, and discrete geometry. He is the co-editor of The Mathematics of Paul Erdős (2013). Joshua Cooper is Professor of Mathematics at the University of South Carolina. He currently serves on the editorial board of Involve. His research interests include spectral hypergraph theory, linear and multilinear algebra, probabilistic combinatorics, quasirandomness, combinatorial number theory, and computational complexity. Glenn Hurlbert is Professor and Chair of the Department of Mathematics and Applied Mathematics at Virginia Commonwealth University. His research interests include universal cycles, extremal set theory, combinatorial optimization, combinatorial bijections and mathematical education, and he is recognized as a leader in the field of graph pebbling.

• 1. Probabilizing Fibonacci numbers Persi Diaconis; 2. On the number of ON cells in cellular automata N. J. A. Sloane; 3. Search for ultraflat polynomials with plus and minus one coefficients Andrew Odlyzko; 4. Generalized Goncharov polynomials Rudolph Lorenz, Salvatore Tringall and Catherine H. Yan; 5. The digraph drop polynomial Fan Chung and Ron Graham; 6. Unramified graph covers of finite degree Hau-Wen Huang and Wen-Ching Winnie Li; 7. The first function and its iterates Carl Pomerance; 8. Erdos, Klarner, and the 3x + 1 problem Jeffrey C. Lagarias; 9. A short proof for an extension of the Erdos–Ko–Rado theorem Peter Frankl and Andrey Kupavskii; 10. The Haight–Ruzsa method for sets with more differences than multiple sums Melvyn B. Nathanson; 11. Dimension and cut vertices William T. Trotter, Bartosz Walczak and Ruidong Wang; 12. Recent results on partition regularity of infinite matrices Neil Hindman; 13. Some remarks on pi Christian Reiher, Vojtech Rodl and Mathias Schacht; 14. Ramsey classes with closure operations Jan Hubicka and Jaroslav Nesetril; 15. Borsuk and Ramsey type questions in Euclidean space Peter Frankl, Janos Pach, Christian Reiher and Vojtech Rodl; 16. Pick's theorem and sums of lattice points Karl Levy and Melvyn B. Nathanson; 17. Apollonian ring packings Adrian Bolt, Steve Butler and Espen Hovland; 18. Juggling and card shuffling meet mathematical fonts Erik D. Demaine and Martin L. Demaine; 19. Randomly juggling backwards Allen Knutson; 20. Explicit error bounds for lattice Edgeworth expansions J. P. Buhler, A. C. Gamst, Ron Graham and Alfred W. Hales.

'Over the past half century, discrete mathematics has had a stunning rise from bargain basement topology to a vital and highly respected part of the mathematical world. Ron Graham has played a critical role in this explosive change, both with his deep results and his leadership in the mathematical community. This work contains beautiful mathematics from some of Ron's many collaborators combined with warm personal reflections on working with Ron.' Joel Spencer, Silver Professor of Mathematics and Computer Science, Courant Institute of Mathematical Sciences, New York