Z/7Z made difficult

here’s a hex board
with seven icons on it;
each icon has seven colors;
the seven permutations of
colors-into-hexes (each icon
has seven hexes) can be
considered as the objects
of a cyclic group.
() = \identity
(1234567) = \psi
(1357246)= \psi^2

(of course one has \psi^7=\identity,
etcetera… the group here is
essentially just integers-mod-7:
{ [0], [1], [2], [3], [4], [5], [6]},
with addition defined by
“cancelling away” multiples
of 7 (forget about the fancily
denoted “permutation structure”
displayed in defining \phi
and just look at the exponents).

the “cycle notation” used here
is *much* under-used, in my opinion.
but we’ll really only need it
for future slides.


    Leave a Reply

    Fill in your details below or click an icon to log in:

    WordPress.com Logo

    You are commenting using your WordPress.com account. Log Out / Change )

    Twitter picture

    You are commenting using your Twitter account. Log Out / Change )

    Facebook photo

    You are commenting using your Facebook account. Log Out / Change )

    Google+ photo

    You are commenting using your Google+ account. Log Out / Change )

    Connecting to %s

%d bloggers like this: