Frontiers of Combinatorics and Number Theory


Editor: Zhi-Wei Sun

Series: Frontiers of Combinatorics and Number Theory

This book is a collection of articles in the first volume of the Journal of Combinatorics and Number Theory. As scheduled this volume consists of three issues and it contains twenty-two contributed papers from eminent experts or active young mathematicians which cover various important topics in number theory and combinatorics. (Imprint: Nova Press)

ISBN: N/A Category:

Table of Contents


Optimal Jumping Patterns;pp. 1-13
(Steve Butler, Ron Graham, and Nan Zang, Dept. of Mathematics, University of California, Los Angeles, USA)

On the Difference Between Solutions of Discrete Tomography Problems;pp. 15-30
(Birgit van Dalen, Mathematisch Institute, University Leiden, The Netherlands)

On the Binomial Convolution of Arithmetical Functions;pp. 31-47
(Laszlo Toth and Pentti Haukkanen, University of Pecs, Hungary and others)

Irrationality Criteria for Infinite Products;pp. 49-57
(Vichian Laohakosol and Kantaphon Kuhapatanakul, Dept. of Mathematics, Kasetsart University, Bangkok, Thailand)

Sums of Triangular Numbers and T-Core Partitions;pp. 59-64
(Ben Kane, Radboud University, Nijmegen, Netherlands)

On Sums of Prime and Triangular Numbers;pp 65-76
(Nanjing University, People’s Republic of China)
(Zhi-Wei Sun, Dept. of Mathematics, Nanjing University, People’s Republic of China)

On Two Conjectures About Mixed Sums of Squares and Triangular Numbers;pp. 77-90
(Ben Kane, Radboud University, Nijmegen, Netherlands)

Some New Theta Function Identities with Applications to Sextenary Quadratic Forms;pp. 91-101
(Ayse Alaca, S. Alaca, and Kenneth S. Williams, School of Mathematics, Carleton University, Ottawa, Ontario, Canada)

Power Values of Palindromes;pp. 103-109
(Javier Cilleruelo, Florian Luca and Igor E. Shparlinski, Universidad Autonoma de Madrid, Espana and others)

On the Structure of Minimal Zero-Sum Sequences With Maximal Cross Number;pp. 111-128
(Alfred Geroldinger and David J. Grynkiewicz, Institut fur Mathematik Und Wissenschaftliches Rechnen, Graz, Austria)

Limit Formulas for Non-Modular Eisenstein Series;pp. 129-135
(Robin Chapman, University of Exeter, UK)

Large Sums of 4k Squares: A Polynomial Approach;pp. 137-156
(Aycse Alaca, Saban Alaca and Kenneth S. Williams, School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada)

On the Number of Representations of Integers by Certain Quadratic Forms, II;pp. 157-187
(Shaun Cooper, Massey University, Auckland, New Zealand)

On a Divisibility Problem Related to Binomial Coefficients;pp. 189-193
(Florian Luca and Gabor Nyul, Universidad Nacional Autonoma de Mexico, Morelia, Michoacan, Mexico and others)

Generators of the Cubic Extension of a Finite Field;pp. 195-209
(Stephen D. Cohen, University of Glasgow, Scotland)

Distribution of Determinant of Matrices With Restricted Entries Over Finite Fields;pp. 211-220
(L.A. Vinh, Harvard University, Cambridge, MA, USA)

Every Polynomial Over a Finite Field of Even Cardinal q > 4 is a Strict Sum of Four Cubes and One Expression A2+A;pp. 221-232
(Luis H. Gallardo,, University of Brest, Brest, Cedex, France)

The Irreducibility of Weighted Sums of Polynomials Whose
Irreducible Factors are Cyclotomic;pp. 233-244
(Carrie Finch and Lenny Jones, Washington and Lee University, Virginia, USA and others)

The GBG-Rank and T-Cores I. Counting and 4-Cores;pp. 245-261
(Alexander Berkovich and Frank Garvan, University of Florida, Gainesville,USA)

The Number of Prime Divisors of a Product of Consecutive Integers;pp. 263-271
(R. Balasubramanian, S. Laishram, T.N. Shorey and R. Thangadurai, The Institute of Mathematical Sciences, Taramani, Chennai, India and others)

On Even Integers Not of the Form 2^k+sigma(m);pp. 273-279
(F. Luca and F. Nicolae, Universidad Nacional Autonoma de Mexico, Morelia, Michoacan, Mexico and others)

Constructing Supersingular Elliptic Curves;pp. 281-285
(Reinier Broker, Microsoft Research, Redmond, WA, USA


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