Journal of Integer Sequences, Vol. 17 (2014), Article 14.2.7

Tilings, Continued Fractions, Derangements, Scramblings, and e

Barry Balof and Helen Jenne
Department of Mathematics
Whitman College
Walla Walla, WA 99362


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),...].
In this paper, we explore those implications through two special types of permutations, namely, derangements and scramblings.

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(Concerned with sequences A000166 A000255 A001048.)

Received October 3 2013. revised versions received December 2 2013; January 6 2014. Published in Journal of Integer Sequences, January 6 2014.

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