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On partitions into figurate numbers and compositions of multipartite numbers. (English) Zbl 1221.05020

Authors’ abstract: We use some \(\mathcal P\)-partitions and the ordinary graph induced by the covering relation of the poset \(\mathcal P\) in order to obtain formulas for the number of some restricted partitions of an ordered \(r\)-tuple of positive integers into vectors whose coordinates are polygonal numbers of a given shape. In particular, we find formulas for the number of partitions of a positive integer into three octahedral numbers.

MSC:

11E25 Sums of squares and representations by other particular quadratic forms
05A17 Combinatorial aspects of partitions of integers
11D25 Cubic and quartic Diophantine equations
11D45 Counting solutions of Diophantine equations
11P83 Partitions; congruences and congruential restrictions
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