Joachim:

We represent value with slips of paper.  We represent ideas with blobs of ink on paper.  There is a mapping, of value to loci, that relates the values {0, 1, 2, ... 99} to a locus in the following string:

0102030405060708091121314151617181922324252627282933435363738394454647484955657585966768697787988990

Easily one may see that "11" is found at the locus 19.  Further, this sub-sequence of characters "11" is found no where else within the larger sequence.  Finally, this sequence is one hundred (100) characters long.  Within this sequence, we see each value {0, 1, 2, ... 99} represented exactly one time; a two character sub-sequence (like "00" for the value zero and "98" for the value ninety eight) for each of these values is found in the sequence, at only one locus.

So, this mapping is simply different from those mappings that are more familiar to you.  It is a symbol sequence, a series but it is not a Taylor Series, it is not the Fibonacci series, etc.

As the strings of my interest are properly bracelets, rings, loops that may freely be rotated, we may rewrite the above one hundred digit string of numbers as

1020304050607080911213141516171819223242526272829334353637383944546474849556575859667686977879889900

We see that this string represents the numeric value of approximately 10 to the ninety nine power (10^99).  Within the digits of this numeric value, we see that pairings of place-value (the one's place, the ten's place; these together make such a pairing of place-value) will represent one of the values {0 .. 99}, and that each member of the set {0 .. 99} will be covered by just one place-value pairing.

Joachim:

It will be important for you to address the issue of shustring lengths.  Not all sequences of digits will have the property that all shustrings lengths are of an equivalent, minimal size.