JP Journal of Algebra, Number Theory and Applications
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Abstract: We use the number of linear extensions of a given poset and
some -partitions, in order to obtain formulas for
the number of some restricted compositions of a given multipartite number into
vectors whose components are integers in arithmetic progression. These formulas
allow us to obtain some relationships between the number of restricted
compositions of a positive integer n
into parts that are either, a sum of three octahedral numbers or square numbers
and the number of restricted compositions of n into parts that are either, a sum of four cubes with two of them
equal or congruent to 1 (mod 6).
Keywords and phrases: Catalan
number, composition, lattice path, linear extension, multipartite number,
octahedral number,
-partition, polygonal number, poset.
