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This book is a collection of articles in the second volume of the Journal of Combinatorics and Number Theory. As scheduled this volume consists of three issues and it contains nineteen contributed papers from eminent experts or active young mathematicians which cover various important topics in number theory and combinatorics.

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.

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 discussed in this compilation include restricted Eisenstein series and certain convolution sums; zeroes of the Hurwitz zeta function in the interval (O,1); prime factorization conditions providing multiplicities in coset partitions of groups; mean value formulas for twisted Edwards curves; binary matrices as morphisms of a triangular category; some diophantine triples and quadruples for quadratic polynomials; codes associated with orthogonal groups; combinatorial sums and series involving inverses of the Gaussian binomial coeffecients; full friendly index sets and full product-cordial index sets of twisted cylinders; and properly charged coloring of two-dimensional arrays.