Correction or disambiguation of A100796 Topological equivalence class of numeral representing n.
Jonathan Post
jvospost3 at gmail.com
Sun Sep 23 02:01:16 CEST 2007
Dr. George Hockney emailed me to say that there is an error (or there
are errors) in:
A100796 Topological equivalence class of numeral representing n.
In comparison with the following text, excerpted from Wikipedia's
definition of "Topology" I admit that my definition is ambiguous.
Does anyone in seqfans have a suggestion for disambiguating or
correcting the seq in question?
Does it fix things if I add the comment: "The lines of the numerals
are assumed to have non-zero width."?
I might also want to add a topological definition of "figure eight" or
it might be preferable to keeping it as is with the hotlink to
Mathworld.
Note that the given lowercase letter topological equivalence can be
turned into an integer sequence in various under the mapping (a, b, c,
d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z)
-> (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 14, 16, 17, 18, 19,
20, 21, 22, 23, 24, 25, 26). However, I find that even more
artificial than my A100796.
-- Jonathan Vos Post
http://en.wikipedia.org/wiki/Topology
A simple introductory exercise is to classify the lowercase letters of
the English alphabet according to topological equivalence. (The lines
of the letters are assumed to have non-zero width.) In most fonts in
modern use, there is a class {a, b, d, e, o, p, q} of letters with one
hole, a class {c, f, h, k, l, m, n, r, s, t, u, v, w, x, y, z} of
letters without a hole, and a class {i, j} of letters consisting of
two pieces. g may either belong in the class with one hole, or (in
some fonts) it may be the sole element of a class of letters with two
holes, depending on whether or not the tail is closed. For a more
complicated exercise, it may be assumed that the lines have zero
width; one can get several different classifications depending on
which font is used. Letter topology is of practical relevance in
stencil typography: The font Braggadocio, for instance, can be cut out
of a plane without falling apart.
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