Geodesic
Tilings, continued fractions, derangements, scramblings, and \(e\)
Journal of integer sequences, Tome 17 (2014) no. 2
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 
@article{JIS_2014__17_2_a0,
     author = {Balof,  Barry and Jenne,  Helen},
     title = {Tilings, continued fractions, derangements, scramblings, and \(e\)},
     journal = {Journal of integer sequences},
     year = {2014},
     volume = {17},
     number = {2},
     zbl = {1295.05005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_2_a0/}
}
TY  - JOUR
AU  - Balof,  Barry
AU  - Jenne,  Helen
TI  - Tilings, continued fractions, derangements, scramblings, and \(e\)
JO  - Journal of integer sequences
PY  - 2014
VL  - 17
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JIS_2014__17_2_a0/
LA  - en
ID  - JIS_2014__17_2_a0
ER  - 
%0 Journal Article
%A Balof,  Barry
%A Jenne,  Helen
%T Tilings, continued fractions, derangements, scramblings, and \(e\)
%J Journal of integer sequences
%D 2014
%V 17
%N 2
%U http://geodesic.mathdoc.fr/item/JIS_2014__17_2_a0/
%G en
%F JIS_2014__17_2_a0
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/