Anzeige
Erschienen in:
2015 | OriginalPaper | Buchkapitel
3. Operations on Species and Operads
verfasst von : Miguel A. Méndez
Erschienen in: Set Operads in Combinatorics and Computer Science
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Abstract
In this chapter operations on species (sum, product, Hadamard product, derivative, and substitution) are introduced by mimicking the analogous operations on exponential generating functions. The operations of substitution and product define two important monoidal categories on species. In this context, operads are defined as monoids in the monoidal category of species with respect to the substitution. Species with a monoidal structure with respect to the operation of product are simply called monoids. As a consequence of the chain rule for species, it is proved that the derivative sends operads into monoids. A construction of families of partially ordered sets from cancellative operads (respectively, cancellative monoids) is obtained. The substitutional (respectively, multiplicative) inverse of the exponential generating function of a cancellative operad (respectively, cancellative monoid) is proved to be the M\"obius generating function of the respective associated family of posets.