Number theory and combinatorics : a collection in honor of the mathematics of Ronald Graham 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