File:Nimbers 0...15 multiplication.svg

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Summary

Description

Multiplication table of Nimbers; compare Sloane's A051775, Sloane's A051910

The nonzero elements form the Cayley table of Z15, as shown below.

Below the dual matrix, showing permuted binary Walsh matrices.
The dark gray fields have an odd binary digit sum, and also form a permuted binary Walsh matrix.
A closer look at these five permutations can be found here.

Image set Operation tables with binary digits (16×16 with dual matrices)
This SVG was created with Inkscape.
Date
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Author
Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".

Cyclic group

Nimber multiplication
 
 1   4   6  14   5   2   8  11   7  10   3  12  13   9  15
 4   6  14   5   2   8  11   7  10   3  12  13   9  15   1
 6  14   5   2   8  11   7  10   3  12  13   9  15   1   4
14   5   2   8  11   7  10   3  12  13   9  15   1   4   6
 5   2   8  11   7  10   3  12  13   9  15   1   4   6  14
 2   8  11   7  10   3  12  13   9  15   1   4   6  14   5
 8  11   7  10   3  12  13   9  15   1   4   6  14   5   2
11   7  10   3  12  13   9  15   1   4   6  14   5   2   8
 7  10   3  12  13   9  15   1   4   6  14   5   2   8  11
10   3  12  13   9  15   1   4   6  14   5   2   8  11   7
 3  12  13   9  15   1   4   6  14   5   2   8  11   7  10
12  13   9  15   1   4   6  14   5   2   8  11   7  10   3
13   9  15   1   4   6  14   5   2   8  11   7  10   3  12
 9  15   1   4   6  14   5   2   8  11   7  10   3  12  13
15   1   4   6  14   5   2   8  11   7  10   3  12  13   9

Table of the same operation, showing the characteristic diagonals of a cyclic group's Cayley table

In both tables it can be seen, that e.g. 4 * 7 = 10

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Date/TimeThumbnailDimensionsUserComment
current19:20, 7 August 2016Thumbnail for version as of 19:20, 7 August 20161,127 × 1,407 (462 KB)wikimediacommons>Stunts1990Made the multiplication indices darker against the transparent background and thus more prominent.

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