
Accession Number : AD0734293
Title : A QAnalog 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 qpartition lattices, which share a number of the structural properties of the lattice of partitions of a set. The qpartition 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