2 papers
math.NT2022
Arithmetic Upper and Lower Bounds for the Denumerant Function
Gerardo Ballesio
We use an old elementary arithmetic argument to find new upper and lower bounds for Sylvester's denumerant function. These bounds are tight enough to get the asymptotic behavior of…
math.CO2015
Counting sub-multisets of fixed cardinality
Sebastiano Ferraris, Alex Mendelson, Gerardo Ballesio +1
This report presents an expression for the number of a multiset's sub-multisets of a given cardinality as a function of the multiplicity of its elements. This is also the number of…