Uhrin's paper

i would really appreciate a detailed explanation of this abstract:

"Self-affine tiles and digit sets via the geometry of numbers"
B. Uhrin
http://rgmia.vu.edu.au/inequalities2001/uhrin/uhrin.html

in english

thanks

-monz

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--- In tuning-math@y..., "monz" <joemonz@y...> wrote:
>
> i would really appreciate a detailed explanation of this abstract:
>
> "Self-affine tiles and digit sets via the geometry of numbers"
> B. Uhrin
> http://rgmia.vu.edu.au/inequalities2001/uhrin/uhrin.html

Are you interested in this abstract in particular, or self-affine tilings, or what, exactly?

--- In tuning-math@y..., "monz" <joemonz@y...> wrote:
>
> i would really appreciate a detailed explanation of this abstract:
>
> "Self-affine tiles and digit sets via the geometry of numbers"
> B. Uhrin
> http://rgmia.vu.edu.au/inequalities2001/uhrin/uhrin.html

R^n is real n-dimensional space, a compact set in such a space is a closed and bounded set, and an expanding matrix is one with all of its eigenvalues greater than one in absolute value. This talk comes from a curious generalization that Jeff Lagarias came up with, which generalizes the idea of a base b expansion to where the base is a matrix. What's the connection to music? I could probably get Jeff to send me a reprint of what he has done if we can't get it off the web.

> From: genewardsmith <genewardsmith@juno.com>
> To: <tuning-math@yahoogroups.com>
> Sent: Sunday, February 03, 2002 1:36 AM
> Subject: [tuning-math] Re: Uhrin's paper
>
>
> --- In tuning-math@y..., "monz" <joemonz@y...> wrote:
> >
> > i would really appreciate a detailed explanation of this abstract:
> >
> > "Self-affine tiles and digit sets via the geometry of numbers"
> > B. Uhrin
> > http://rgmia.vu.edu.au/inequalities2001/uhrin/uhrin.html
>
> R^n is real n-dimensional space, a compact set in such a space
> is a closed and bounded set, and an expanding matrix is one
> with all of its eigenvalues greater than one in absolute value.
> This talk comes from a curious generalization that Jeff Lagarias
> came up with, which generalizes the idea of a base b expansion
> to where the base is a matrix.

thanks, gene ... but i still don't understand

what's an eigenvalue?

> What's the connection to music?

ah ... that's for y o u to tell m e !!!

i'm just hunting down stuff that discusses lattices,
so that i can learn more about them

BTW ... i took a look at the first couple of chapters from
the Conway/Sloane book you recommended (_Sphere Packings..._),
but don't understand much of that either :(

-monz

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