Date: Sep 8, 2013 8:43 AM
Author: Jussi Piitulainen
Subject: Re: abelian square
Dieter von Holten writes:

> hi folks,

>

> i found 'abelian squares' in the context of patterns of n symbols of

> length 2n like 'abcd.cdba' where 'cdba' is a permutation of the

> first half 'abcd'.

> however, in those texts it is not explained (maybe just not clear

> enough for me) what is 'abelian' and where is the 'square' ??

I guess abcd.cdba = abcd.abcd = (abcd)^2 if xy = yx (the operation

indicated by writing things next to each other is commutative). I'm

also assuming that xy = x.y (the dot indicates the same operation as

writing things next to each other).

Abelian means commutative (that the order of the operands of an

operator doesn't matter), and square stuff means stuff raised to the

second power (the superscript 2).