Compositions of ▫$n$▫ satisfying some coprimality conditions
Bubboloni, Daniela ; Luca, Florian ; Spiga, Pablo
An ▫$\ell $▫-composition of ▫$n$▫ is a sequence of length ▫$\ell $▫ of positive integers summing up to ▫$n$▫. In this paper, we investigate the number of ▫$\ell $▫-compositions of ▫$n$▫ satisfying ...two natural coprimality conditions. Namely, we first give an exact asymptotic formula for the number of ▫$\ell $▫-compositions having the first summand coprime to the others. Then, we estimate the number of ▫$\ell $▫-compositions whose summands are all pairwise coprime.
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