Möbius polynomial species
The authors introduce ``Möbius species'', which can be considered as a special class of weighted species. Roughly speaking, the objects of consideration are posets with minimal element \(\widehat 0\) and maximal element \(\widehat 1\), which are given the weight \(\mu(\widehat0,\widehat1)\), the Möbius function of \(\widehat0\) and \(\widehat1\). A theory for these species is developed which parallels the usual theory (but, of course, has stronger results because of the special nature of these species). Things are set up in a way so that some identities for symmetric functions can be given a species theoretic interpretation.
scientific article; zbMATH DE number 1062451