Geodesic
On the distribution of some characteristics of a quasimonotone mapping
Diskretnaya Matematika, Tome 22 (2010) no. 3, pp. 8-19
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We consider a mapping of a discrete circle into itself preserving the order inside triples of points. We describe the structure of the graph of the mapping and investigate the distributions of the number and lengths of its cycles. 
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M. I. Tolovikov. On the distribution of some characteristics of a quasimonotone mapping. Diskretnaya Matematika, Tome 22 (2010) no. 3, pp. 8-19. http://geodesic.mathdoc.fr/item/DM_2010_22_3_a1/

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