An ℓ-composition of n is a sequence of length ℓ of positive integers summing up to n. In this paper, we investigate the number of ℓ-compositions of n satisfying two natural coprimality conditions. Namely, we first give an exact asymptotic formula for the number of ℓ-compositions having the first summand coprime to the others. Then, we estimate the number of ℓ-compositions whose summands are all pairwise coprime. © 2012 Elsevier Inc.
Bubboloni, D., Luca, F., Spiga, P. (2012). Compositions of n satisfying some coprimality conditions. JOURNAL OF NUMBER THEORY, 132(12), 2922-2946 [10.1016/j.jnt.2012.06.012].
Compositions of n satisfying some coprimality conditions
SPIGA, PABLO
2012
Abstract
An ℓ-composition of n is a sequence of length ℓ of positive integers summing up to n. In this paper, we investigate the number of ℓ-compositions of n satisfying two natural coprimality conditions. Namely, we first give an exact asymptotic formula for the number of ℓ-compositions having the first summand coprime to the others. Then, we estimate the number of ℓ-compositions whose summands are all pairwise coprime. © 2012 Elsevier Inc.
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