Geodesic
Shuffling of Linear Orders
Canadian mathematical bulletin, Tome 38 (1995) no. 2, pp. 223-229

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DOI

A linearly ordered set A is said to shuffle into another linearly ordered set B if there is an order preserving surjection A —> B such that the preimage of each member of a cofinite subset of B has an arbitrary pre-defined finite cardinality. We show that every countable linearly ordered set shuffles into itself. This leads to consequences on transformations of subsets of the real numbers by order preserving maps.
DOI : 10.4153/CMB-1995-032-1
Mots-clés : 06A05 
Orr, John Lindsay. Shuffling of Linear Orders. Canadian mathematical bulletin, Tome 38 (1995) no. 2, pp. 223-229. doi: 10.4153/CMB-1995-032-1
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     title = {Shuffling of {Linear} {Orders}},
     journal = {Canadian mathematical bulletin},
     pages = {223--229},
     year = {1995},
     volume = {38},
     number = {2},
     doi = {10.4153/CMB-1995-032-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-032-1/}
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