Accession Number : AD0271038

Title :   ON LINEAR EXTENSIONS OF THE CANONICAL PARTIAL ORDER IN THE N-CUBE Q TO THE NTH POWER

Corporate Author : LOCKHEED MISSILES AND SPACE CO SUNNYVALE CALIF

Personal Author(s) : HU,SZE-TSEN

Report Date : OCT 1961

Pagination or Media Count : 1

Abstract : The enumeration of the canonical truth functions is considered. A method of getting all of the canonical truth functions is given. The canonical partial order is studied in the Q to the Nth power and proven that Q to the Nth power becomes a lattice with respect to the canonical partial order. A recurrent method of constructing the lattice structure of Q to the Nth power is also given. The fact is established that the canonical partial order in Q to the Nth power can be extended to a linear order which will be called the principal linear order of Q to the Nth power. Since this linear order of Q to the Nth power can be defined by an injective canonical weight function, those linear orders of Q to the Nth power which can be defined by injective weight functions can be studied. A recurrent method of finding these linear orders of Q to the Nth power is given. These linear orders are applied to the problem of finding all canonical truth functions. (Author)

Descriptors :   *FUNCTIONS(MATHEMATICS), *LINEAR SYSTEMS, *MATHEMATICAL LOGIC, ALGEBRA, COMPLEX VARIABLES, CRYSTAL LATTICES, INEQUALITIES, NUMBER THEORY, REAL VARIABLES

Distribution Statement : APPROVED FOR PUBLIC RELEASE