TITLE: Occurrences of D. H. Lehmer's 10-th degree polynomial
QUESTION [13 upvotes]: Salem numbers and Lehmer's minimum height problem are venerated not only in number theory and diophantine analysis, where they are considered naturally interesting for their own sake, but also in fields such as hyperbolic geometry and holomorphic dynamics. As is so well known, the least known Salem number is a root $1.176280\ldots$ of the following monic reciprocal $10$-th degree $\{-1,0,1\}-$polynomial discovered way back in 1933 by D. H. Lehmer in his work on primality testing:
$$
x^{10} + x^9 - x^7 - x^6 - x^5 - x^4 - x^3 + x + 1.
$$
I am interested in seeing any mathematical contexts or computations through which this particular polynomial shows up, apparently accidental occurrences included (not to say preferred). 
Here is an example from topology: this is the Alexander polynomial of infinitely many knots, including the $(-2,3,7)$-pretzel knot.

REPLY [7 votes]: Here's a paper of McMullen where the Lehmer polynomial shows up (see Theorem 1.2 there): 
http://www.math.harvard.edu/~ctm/papers/home/text/papers/blowup/blowup.pdf

REPLY [5 votes]: well, this link will direct you to just under 300 scholarly articles on Lehmer's polynomial:
http://scholar.google.com/scholar?q=polynomial+lehmer&btnG=&hl=en&as_sdt=2005&sciodt=0%2C5&cites=18047953845360790641&scipsc=1
(oh, and I added the big-list tag to this question, I guess that is appropriate :)

a small selection:

The
Lehmer polynomial and pretzel links
What is Lehmer's Number?
Heights of polynomials and entropy in algebraic dynamics
On the
distribution of the roots of a polynomial with integral
coefficients
Primes in sequences associated to polynomials (after Lehmer)
Lehmer's
problem for compact Abelian groups
Higher
Mahler measure for cyclotomic polynomials and Lehmer's question
Lehmer's Conjecture for
Hermitian Matrices over the Eisenstein and Gaussian Integers
Solved
and unsolved problems on polynomials
Polynomials with restricted coefficients and prescribed noncyclotomic factors
A seventeenth-order polylogarithm ladder
Lehmer's question, knots and surface dynamics