# Accession Number:

## AD0271038

# Title:

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

# Descriptive Note:

# Corporate Author:

## LOCKHEED MISSILES AND SPACE CO SUNNYVALE CALIF

# Personal Author(s):

# Report Date:

## 1961-10-01

# Pagination or Media Count:

## 1.0

# 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