Geodesic
Tilings, continued fractions, derangements, scramblings, and $e$
Journal of integer sequences, Tome 17 (2014) no. 2.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In a recent book, Benjamin and Quinn ask about the combinatorial implications of Euler's continued fraction $e$ = [2,(1,1),(1,2),(2,3),(3,4),$\dots $]. In this paper, we explore those implications through two special types of permutations, namely, derangements and scramblings.
Classification : 05A05, 05A15, 05B45
Keywords: chessboard tiling, continued fraction, linear recurrence, derangement, permutation combinatorics 
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     author = {Balof, Barry and Jenne, Helen},
     title = {Tilings, continued fractions, derangements, scramblings, and $e$},
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Balof, Barry; Jenne, Helen. Tilings, continued fractions, derangements, scramblings, and $e$. Journal of integer sequences, Tome 17 (2014) no. 2. http://geodesic.mathdoc.fr/item/JIS_2014__17_2_a0/