File:Boolean partition matrices.svg

Summary

Description

The 67 subgroups of Z24 (compare Subgroups of nimber addition), represented by logical matrices
The red squares (binary ones) mark the position of the subgroups' elements in the Cayley table. (File:Z2^4; Cayley table; binary.svg)

These matrices can also be read as partitions of a 16 element set,
or as sec matrices of Boolean functions (compare: File:Boolean functions like 1001 0110.svg).
(Actually these matrices are the intersection of partition matrices and sec matrices.)

The increasing numbers on the left (Sloane's A190939) are the unique odd numbers in each sec (among the numeric values of the Boolean functions in the sec, to be precise).
The numbers on the right (Sloane's A227963) are the smallest in the sec.

Here the same is shown for n=0...2824.

The file is shown below.

Python dict of these 67 objects represented as binary vectors and as partitions: https://pastebin.com/pDz53JXt

This SVG was created with Inkscape.
Source Own work
Author
Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".
Permission
(Reusing this file)
Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
Category:Self-published work#Z2^4;%20subgroups%20list.svgCategory:PD-self#Z2^4;%20subgroups%20list.svg
Other versions

See also:
File:Z2^4;_subgroups_list_(top_rows).svg

File:Z2^4;_subgroups_list_(top_rows_rearranged_by_digit_sum).svg

File

This description page is about the file on the left. In the file on the right the equivalence blocks are colored, to make them easily recognizable.

Gray numbers are the indices.
Increasing numbers on the left form Sloane's A190939. These are the unique odd numbers in each family.
The numbers on the right form Sloane's A227963. These are the smallest numbers in each family.


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Category:Family matrices of 4-ary Boolean functions Category:Equivalence relation matrix Category:Seals with arity 4 Category:Colexicographic order