PARTIÇÕES, MATRIZES DE DUAS LINHAS E PARTIÇÕES T-QUADRADAS

Abstract

A natural number m is said to admit a t- squared partition if we can find c₁...,c_t  em N, such that

m = ( c₁+c₂+... + c_t)² +  2(c₁²+c₂²+... + c_t ²).

In this paper, we present a complete characterization of integers that admit t-squared partitions, and we will also introduce a correspondence between the number of partitions of n, both with and without constraints, and the number of representations of integers m in (1, n²) as t-squared partitions.