Accession Number : AD0734293

Title :   A Q-Analog of the Partition Lattice,

Corporate Author : NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS

Personal Author(s) : Dowling,Thomas A.

Report Date : NOV 1971

Pagination or Media Count : 27

Abstract : The report describes for any prime power q a general class of geometric lattices, called q-partition lattices, which share a number of the structural properties of the lattice of partitions of a set. The q-partition lattice is shown to be isomorphic to the lattice of closed sets of a subgeometry of projective geometry over GF(q). The Mobius function and characteristic polynomial are obtained, and an identity and recursion for the Whitney numbers derived. An application is given to the enumeration of factorial designs with no main effects or second order interactions confounded. (Author)

Descriptors :   (*SET THEORY, COMBINATORIAL ANALYSIS), PROJECTIVE GEOMETRY, ALGEBRA, RECURSIVE FUNCTIONS, POLYNOMIALS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE