Annals of Combinatorics 3 (1999) 115-130
Stacked Lattice Boxes
George E. Andrews
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA
Received October 20, 1998
AMS Subject Classification: 05A19, 05A17, 11P81, 11P82
Abstract.We study the number of solutions of the Diophantine equation n = x1 x2 + x2 x3 + x3 x4 + ... + xk xk+1. The combinatorial interpretation of this equation provides the name ``stacked lattices boxes''. The study of these objects unites three separate threads in number theory: (1) the Liouville methods, (2) MacMahon's partitions with k different parts, (3) the asymptotics of divisor sums begun by Ingham.
Keywords: stacked lattice boxes, Liouville methods, partitions, divisor sums