On the Foundation of Combinatorial Theory. X. A Categorical Setting for Symmetric Functions

This paper examines surface gravity waves in a shallow channel with periodic or random bottom irregularities. Three types of bottom topography are distinguished, allowing a simplification of the basic shallow-water-wave equations. For two of them, asymptotic equations of the Korteveg-de Vries type are derived (the third type has been considered earlier by other authors).     

Sistemi di coefficienti sezionali I

The notion of section coefficients is a generalization of the notion of multinomial coefficients. Our definition is motivated both by combinatorial examples and by the analogy with the theory of coalgebras. We develop an analysis of fundamental properties of systems of section coefficients and prove finiteness theorems related to the classical finiteness theorem of coalgebras.