l(b,0) -> l(ab,0) -> l(a,0) -> l(b,1)

l(ab,0) -> l(a,0) -> l(b,1) -> l(ab,1)

l(a,0) -> l(b,1) -> l(ab,1) -> l(a,1)

????????????

l(c,0) -> l(bc,0) -> l(b,0) -> l(c,1)

l(c,0) -> l(abc,0) -> l(ab,0) -> l(c,1)

l(bc,0) -> l(abc,0) -> l(a,0) -> l(bc,1)




d->de->e

f->ef->e

df->def->e ??df decomposable???

d->def->ef

f->def->de

?????????

. a b c ab bc abc

a 0 0 0
b 1 0 0
c 1 0 1
ab 0 0 0
bc 1 0 0
abc 0 0 0

. d e f de ef def

d 0 1 1
e 0 0 0
f 1 0 1
de 0 0 0
ef 0 0 0
def 0 0 0

??so it looks like ab and bc are going to have to match up with e and def (?not nec resp?) ...

let's try:

ab_[j+1] = e_j
bc_[j+1]= def_j
a_j = d_j
c_[j+1] = f_j
b_[j+1] = de_j
abc[j+1] = ef_j

that one seems to work ... ??but let's try to make an exhaustive list here....

a = f
b = ef
c = d
ab = e
bc = def
abc = de
--
a = ef
b = d
c = de
ab = def
bc = e
abc = f
--
a = de
b = f
c = ef
ab = def
bc = e
abc = d
--

a c
b abc
ab bc

a b bc c abc ab ????...

a bc b abc ab abc ???....

(ab bc) (a abc) (b c) ?????

???seems rigid????? or something??....



irreducible quiver rep = simple root??

indecomposable quiver rep = positive root??

???......