Frontiers in Combinatorics and Number Theory. Volume 4


Zhi-Wei Sun (Editor)
Department of Mathematics, Nanjing University, P.R. China

Series: Frontiers of Combinatorics and Number Theory
BISAC: MAT022000

This book contains papers on topics in combinatorics (including graph theory) or number theory. The subject areas within correspond to the MSC (Mathematics Subject Classification) codes 05, 11, 20D60, and 52.

Some topics included in this compilation are pseudorandom binary functions on rooted plane trees; class number one criteria for real quadratic fields with discriminant k2p2¡Ó4p; some product-to-sum identities; a zeta function for juggling sequences; divisibility properties of hypergeometric polynomials; the distance between perfect numbers; a new proof of a theorem of Hamidoune avoiding; conjectures on the monotonicity of some arithmetical sequences; complexity of trapezoidal graphs with different triangulations; applications of shuffle products of multiple zeta values in combinatorics; the invariant area formulas and lattice point bounds for the intersection of hyperbolic and elliptic regions; and product-cordial index set for Cartesian products of a graph with a path. (Imprint: Nova)



Table of Contents

Pseudorandom Binary Functions on Rooted Plane Trees
(Katalin Gyarmati, Pascal Hubert, and Andras Sarkozy)

Class Number One Criteria for Real Quadratic Fields with Discriminant k2p2¡Ó4p
(Richard A. Mollin and Anitha Srinivasan)

Some Product-to-Sum Identities
(Saban Alaca, Lerna Pehlivan, and Kenneth S. Williams)

A Zeta Function for Juggling Sequences
(Carten Elsner, Dominic Klyve, and Erik R. Tou)

A Quadratic Twist of the Elliptic Curve y2=x(x-1)(x-Ć)
(Ivic Gusic, Luka Lasic, and Petra Tadic)

Divisibility Properties of Hypergeometric Polynomials
(Clemens Fuchs and T. N. Shorey)

For Which p-Adic Integers x Can Ʃk(x/k)-1 Be Defined?
(M. Davis)

On the Distance between Perfect Numbers
(Philippe Ellia)

A New Proof of a Theorem of Hamidoune Avoiding Cayley Graphs
(Ram Krishna Pandey)

On Some Conjectures on the Monotonicity of Some Arithmetical Sequences
(Florian Luca and Pantelimon Stanica)

Complexity of Trapezoidal Graphs with Different Triangulations
(S. N. Daoud and A. Elsonbaty)

A Note to Zhi-Wei Sun’s Supercongruences on Binomial Coefficients
(Ching-Cheong Lee, Wodan Ling, Nan Wu, and Minjue Xu)

Applications of Shuffle Products of Multiple Zeta Values in Combinatorics
(Mingking Eie, Tung-Yang Lee, Yao Lin Ong)

On Invariant Area Formulas and Lattice Point Bounds for the Intersection of Hyperbolic and Elliptic Regions
(Mike Bennett, Krill Y. Lazebnik, Patrick X. Rault, and Jeffrey A. Singer)

Product-Cordial Index Set for Cartesian Product of a Graph with a Path
(Wai Chee Shiu)

Infinitely Many Congruences for Broken 2-Diamond Partitions Modulo 3
(Cristian-Silviu Radu and James A. Sellers)


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