Periodic Patterns of Signed Shifts
2013 ◽
Vol DMTCS Proceedings vol. AS,...
(Proceedings)
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Keyword(s):
Tent Map
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International audience The periodic patterns of a map are the permutations realized by the relative order of the points in its periodic orbits. We give a combinatorial description of the periodic patterns of an arbitrary signed shift, in terms of the structure of the descent set of a certain transformation of the pattern. Signed shifts are an important family of one-dimensional dynamical systems. For particular types of signed shifts, namely shift maps, reverse shift maps, and the tent map, we give exact enumeration formulas for their periodic patterns. As a byproduct of our work, we recover some results of Gessel and Reutenauer and obtain new results on the enumeration of pattern-avoiding cycles.
2011 ◽
Vol DMTCS Proceedings vol. AO,...
(Proceedings)
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2001 ◽
Vol 01
(03)
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pp. 299-338
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2007 ◽
Vol 14
(5)
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pp. 615-620
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2007 ◽
Vol DMTCS Proceedings vol. AH,...
(Proceedings)
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Keyword(s):
2010 ◽
Vol DMTCS Proceedings vol. AM,...
(Proceedings)
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2007 ◽
Vol 55
(1)
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pp. 53-62
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1996 ◽
Vol 06
(04)
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pp. 725-735
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