Abstract
The determination of the degeneracy of a given energy level of an N-dimensional isotropic quantum oscillator that is perturbed by an isotropic quartic potential energy term leads to the question to enumerate the number of nonnegative integer solutions ( n 1,…, n N ), n 1 ⩾ ··· ⩾ n N , of the system n = n 1 + ··· + n N , m = n 1 2 + ··· + n N 2, as was shown recently by Louck and Metropolis. The present paper shows the partial reduction of this question to a similar one which is solved in the literature, precisely for N ⩽ 8, asymptotically for N > 8.
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