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

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