On an inequality in a 1970 paper of R. L. Graham
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J.-P. Allouche
Abstract
Having recently come across a 1970 paper of R. L. Graham about cubenumbering and its generalizations, we found that one proof uses an inequality about the summatory function of the sum of binary digits of integers. Graham gave a very elegant and somehow unexpected proof of this inequality. We propose a more “pedestrian”- and somehow more standard-proof of this inequality, as well as questions about possible generalizations.
Abstract
Having recently come across a 1970 paper of R. L. Graham about cubenumbering and its generalizations, we found that one proof uses an inequality about the summatory function of the sum of binary digits of integers. Graham gave a very elegant and somehow unexpected proof of this inequality. We propose a more “pedestrian”- and somehow more standard-proof of this inequality, as well as questions about possible generalizations.
Kapitel in diesem Buch
- Frontmatter I
- Foreword V
- Contents VII
- Multivariate difference Gončarov polynomials 1
- On an inequality in a 1970 paper of R. L. Graham 21
- Arithmetic progressions in sumsets of sparse sets 27
- Multidimensional Padé approximation of binomial functions: equalities 35
- Graphical enumeration and stained glass windows, 1: rectangular grids 65
- Two extensions of Hilbert’s cube lemma 99
- The Gallai–Ramsey number for a tree versus complete graphs 109
- On Levine’s notorious hat puzzle 115
- Recurrence ranks and moment sequences 167
- On weak twins and up-and-down subpermutations 187
- Distance graphs and arithmetic progressions 203
- Consecutive primes which are widely digitally delicate 209
- Spanning trees and domination in hypercubes 249
- Rook domination on hexagonal hexagon boards 259
- Strongly image partition regular matrices 267
- Introducing shift-constrained Rado numbers 285
- Mertens’ prime product formula, dissected 297
- Curious convergent series of integers with missing digits 311
- A note on Carmichael numbers in residue classes 321
- Tilted corners in integer grids 329
- Remembrances 339
- A selected bibliography of Ron Graham 355
Kapitel in diesem Buch
- Frontmatter I
- Foreword V
- Contents VII
- Multivariate difference Gončarov polynomials 1
- On an inequality in a 1970 paper of R. L. Graham 21
- Arithmetic progressions in sumsets of sparse sets 27
- Multidimensional Padé approximation of binomial functions: equalities 35
- Graphical enumeration and stained glass windows, 1: rectangular grids 65
- Two extensions of Hilbert’s cube lemma 99
- The Gallai–Ramsey number for a tree versus complete graphs 109
- On Levine’s notorious hat puzzle 115
- Recurrence ranks and moment sequences 167
- On weak twins and up-and-down subpermutations 187
- Distance graphs and arithmetic progressions 203
- Consecutive primes which are widely digitally delicate 209
- Spanning trees and domination in hypercubes 249
- Rook domination on hexagonal hexagon boards 259
- Strongly image partition regular matrices 267
- Introducing shift-constrained Rado numbers 285
- Mertens’ prime product formula, dissected 297
- Curious convergent series of integers with missing digits 311
- A note on Carmichael numbers in residue classes 321
- Tilted corners in integer grids 329
- Remembrances 339
- A selected bibliography of Ron Graham 355
