Characterizations of the generalized Wu- and Kosmulski-indices in Lotkaian systems

We define the generalized Wu- and Kosmulski-indices, allowing for general parameters of multiplication or exponentiation. We then present formulae for these generalized indices in a Lotkaian framework.Next we characterise these indices in terms of their dependence on the quotient of the average number of items per source in the m-core divided by the overall average (m is any generalized Wu- or Kosmulski-index).As a consequence of these results we show that the fraction of used items (used in the definition of m) in the m-core is independent of the parameter and equals one divided by the overall average.

► We define and prove formulae for the generalized Wu- and Kosmulski-indices, allowing for general parameters of multiplication or exponentiation.
► Next we characterise these indices in terms of the average number of items per source in the m-core.
► We show that the fraction of used items in the m-core equals one divided by the overall average.