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A262029
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Numbering of the 32 radial streets on a prospect of the city of Karlsruhe (Baden), Germany from 1721.
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1
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1, 3, 5, 7, 9, 26, 20, 23, 16, 24, 21, 25, 13, 12, 11, 27, 10, 17, 22, 32, 15, 28, 18, 30, 14, 29, 19, 31, 8, 6, 4, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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The numbering is in the counterclockwise direction, beginning in the south (S on the 32-wind compass rose, see the link).
This numeration appears on the copperplate-engraving by Heinrich Schwartz entitled "Prospect der Furst Marggraf Baaden Durlach neuerbauten Residenz Statt Carolsruhe, 1721", Badisches Landesmuseum, Karlsruhe.
Opposite numbers a(j) and a(16+j), for j=1..16, sum to 11, 20, 27, 39, 24, 54, 38, 53, 30, 53, 40, 56, 21, 18, 15, 29, a partition of 32*33/2 = 528.
The rationale behind this numbering (except for the brighter ten-street sector in the south, corresponding to the first five and last four numbers) remains a mystery to the author.
This is a contribution on the occasion of the 300th anniversary of the foundation of Karlsruhe in 1715.
This element of the symmetric group S_32 has cycle type (1^2, 3^2, 10, 14): (1) (2, 3, 5, 9, 16, 27, 19, 22, 28, 31, 4, 7, 20, 32) (6, 26, 29, 8, 23, 18, 17, 10, 24, 30) (11, 21, 15) (12, 25, 14) (13). - Wolfdieter Lang, Oct 13 2015
In the Universität Bern link (found by Hans Havermann) two prospects of Karlsruhe are shown, and the legend of the upper one gives the names of people assigned to the streets (alleys and lanes) numbered from 1 to 32. See the Legend link. Peter Luschny commented (Oct 14 2015) "The paths are named after some knights and other noble men which are listed in the margins and what appears as an arbitrary numbering is used to reference these names." - Wolfdieter Lang, Oct 16 2015
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LINKS
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CROSSREFS
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KEYWORD
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nonn,fini,full,less
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AUTHOR
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STATUS
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approved
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