## Smallest Known Measures of Two-Variable Polynomials

The following list records all known polynomials in two variables having Mahler's measure greater than 1 and less than 1.37. Most polynomials come from one of the following five families of six-term polynomials, or hexanomials:

P(a,b) = xmax(a-b,0)((1-xa) + (1-xb)y + xb-a(1-xa)y2)/(1-x),
Q(a,b) = xmax(a-b,0)((1+xa) + (1+xb)y + xb-a(1+xa)y2),
R(a,b) = xmax(a-b,0)((1+xa) + (1-xb)y - xb-a(1+xa)y2),
S(a,b,e) = 1 + (xa+e)(xb+e)y + xa+by2,
T(f(x)) = f(x) + f*(x)y.
In the last case, f is a trinomial and f* denotes the reciprocal polynomial of f. If f is reducible, the coefficients of its noncyclotomic part are shown in brackets.

A few sporadic polynomials are labeled using the rows of their coefficient matrix, for example, the third polynomial in the list denotes the polynomial 1+x+(1-x2+x4)y + (x3+x4)y2.

```  1.)  1.2554338662666087457   P(2,3)
2.)  1.2857348642919862749   P(1,3) or P(2,1)
3.)  1.3090983806523284595   [++000, +0-0+, 000++]
4.)  1.3156927029866410935   P(3,5)
5.)  1.3247179572447460260   T(1+x-x3)
6.)  1.3253724973075860349   P(3,4)
7.)  1.3320511054374193142   P(2,5)
8.)  1.3323961294587154121   S(1,3,+)
9.)  1.3381374319388410775   P(3,2)
10.)  1.3399999217381835332   P(4,7)
11.)  1.3405068829308471079   P(3,1)
12.)  1.3497161046696958653   T(1+x2-x7); [+++0--]
13.)  1.3500148321630142650   P(3,7)
14.)  1.3503169790598690950   S(1,4,-)
15.)  1.3511458956697046903   P(4,5)
16.)  1.3524680625188602961   P(5,9)
17.)  1.3536976494626355711   Q(1,6)
18.)  1.3567481051456008311   P(4,3)
19.)  1.3567859884526454967   P(5,8)
20.)  1.3581296324044179208   [++00000, +0---0+, 00000++]
21.)  1.3585455903960511404   P(4,1)
22.)  1.3592080686995589268   P(4,9)
23.)  1.3598117752819405021   P(6,11)
24.)  1.3598158989877492950   S(1,6,+)
25.)  1.3599141493821189216   T(1+x+x8); [+0-+0-+]
26.)  1.3602208408592842371   P(5,7)
27.)  1.3627242816569882815   P(5,6)
28.)  1.3636514981864992177   S(3,5,+)
29.)  1.3641995455827723418   T(1-x2+x5)
30.)  1.3644358117806362770   [+000, 00++, ++00, 000+]
31.)  1.3645459857899151366   P(7,13)
32.)  1.3646557293930641449   P(5,11)
33.)  1.3650623157174417179   S(2,7,-)
34.)  1.3654687370557201592   P(5,4)
35.)  1.3659850533667936783   [++000, ++0-0, 00000, 0-0++, 000++]
36.)  1.3661459663116649518   P(5,3)
37.)  1.3665709746056369455   P(5,2)
38.)  1.3668078899273126149   P(5,1)
39.)  1.3668830708592258921   R(1,5)
40.)  1.3669909125179202255   P(7,12)
41.)  1.3677988580117157740   P(8,15)
42.)  1.3678546316653002345   T(1+x4+x11); [+-0+0-+0-+]
43.)  1.3681962517212729703   P(6,13)
44.)  1.3682140096679950123   P(1,9)
45.)  1.3683434385467330804   [++00000, ++0-0++, 00000++]
46.)  1.3687474425069274154   P(6,7)
47.)  1.3689491694959833864   P(7,11)
48.)  1.3697823199880122791   S(1,9,+)
```