Number Theory and Combinatorics: A Collection in Honor of the Mathematics of Ronald Graham (De Gruyter Proceedings in Mathematics)

Over a career that spanned 60 years, Ronald L. Graham (known to all as Ron) made significant contributions to the fields of discrete mathematics, number theory, Ramsey theory, computational geometry, juggling and magical mathematics, and many more. Ron also was a mentor to generations of mathematicians, he gave countless talks and helped bring mathematics to a wider audience, and he held signifi cant leadership roles in the mathematical community. This volume is dedicated to the life and memory of Ron Graham, and includes 20-articles by leading scientists across a broad range of subjects that refl ect some of the many areas in which Ron worked. * Original contributions by leading experts in combinatorics and number theory * Includes essays and memories of Professor Graham from those that knew him * Of interest to researchers and graduate students working in combinatorics and number theory. Foreword Contents Multivariate difference Gončarov polynomials On an inequality in a 1970 paper of R. L. Graham Arithmetic progressions in sumsets of sparse sets Multidimensional Padé approximation of binomial functions: equalities Graphical enumeration and stained glass windows, 1: rectangular grids Two extensions of Hilbert’s cube lemma The Gallai–Ramsey number for a tree versus complete graphs On Levine’s notorious hat puzzle Recurrence ranks and moment sequences On weak twins and up-and-down subpermutations Distance graphs and arithmetic progressions Consecutive primes which are widely digitally delicate Spanning trees and domination in hypercubes Rook domination on hexagonal hexagon boards Strongly image partition regular matrices Introducing shift-constrained Rado numbers Mertens’ prime product formula, dissected Curious convergent series of integers with missing digits A note on Carmichael numbers in residue classes Tilted corners in integer grids Remembrances A selected bibliography of Ron Graham