ON THE FOUNDATIONS OF COMBINATORIAL THEORY. IV. FINITE VECTOR SPACES AND EULERIAN GENERATING FUNCTIONS.
HARVARD UNIV CAMBRIDGE MASS DEPT OF STATISTICS
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The paper studies combinatorial aspects of the lattice of subspaces of a vector space over a finite field and its use in deriving classical and new q-identities. Set theoretic interpretations of these identities are given in terms of the enumeration of vector spaces and linear transformations. The incidence algebra of a partially ordered set is shown to be a true generalization of the notion of a generating function and Eulerian generating functions are applied to count a variety of vector space objects. Combinatorial interpretations are provided for general q-difference equations. Author
- Theoretical Mathematics