Details Page for 0.1667

Complete Solution is Known:

MSV File: q-0.1667.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₃₄₀(0.1667):

Q = <a,b,c,d,e,f,g,h,i,j,k | a²=1, b³=b, bc=ab, c²=b², d²=1, be=bd, e²=b², cf=ab²f, f²=b², bg=ab, cg=ac, eg=ae, fg=af, g²=ag, bh=ab, ch=b², eh=ce, fh=ab²f, gh=ah, h²=b², b²i=i, ci=ai, ei=di, gi=ai, hi=ai, i²=b², b²j=j, cj=aj, ej=dj, gj=aj, hj=aj, j²=b², b²k=k, ck=ak, ek=dk, gk=ak, hk=ak, k²=b²>

P = {a, b², ad, cd, adef, dg, ah}

Phi = 1 a 1 1 bd bd abd b b a c d e bd bd ab b f g h abd abd bdf ab b b b²f b²d b²d abdf bdf ab² abd ab²f b²f b²f b²d ab²d bdf b b abd abd b²f b²d ab² ab² bdf bdf bf abf ab²df b²d b²d abdf b i bf ai bdi ab²df b²df bi bi abf b²d b di abdi b²df b²f b²f ai abf abdf b b²d b²d b²df bi bi abf bdf bdf abdf afi abd abd ab²f ab² ab² di bdf bdf b²d b²f ab²f b b abdf abdf i b²d b²f b²f ab²df ab di di abd b²d ai ab² b²f bdi bdf bd i b²d b²d ab² ab² bdi afi abd abd i i abdfi bfi abdi abdi b²d ai adi adi abfi ab² bdi bdi j abd abd b b ab² abdfi b²d b²d ab²df j ab b²f ab² ab² ai b²d aj j b b abf bdj bdj b²d aj ab² ab² afi b²f b²f bdfi ab²d ab²d bfi j b abd abd abdj bj bdf ab² abf abf bdj bdj ab²df b²df b ab² i abf dfi dfi bdi abdi abdi ab² ab² b²d b²d b afi ab²df ab²df b²f b²f fj adj di afi adfi fi ab²df b²f j j aj di abdf abd abd ab² ab² afj j adi bdf adj bi b²f ab²f ab² j abdf bdf i adfi bi bi ab²df ab²df di abd b²d abf b²f bj bdi ab²df ab²df adj b²d b²d afi bj abfj abdi afj abdfi bd i i bfi bfi abdi abdi abd dj dfj abf bdij bdfj bdi b²d adj abd b b ab² ab² abdj b²d ab²df ab²df ab b fij ab² ab² ij adij abfi aj b b abf bfj abdfi abdfi adij j aj afj afj bdfi ab²d abj bfi bfi b b abd abd fij bdf bdf abdfij j adj adj adij dfj bj b abfi bdfi abi abdfij j fi bdf bdj bfi b²d b²d dfj dfj ab²df k bdj bdj abi abf abdfi di aj b fij abfj abi abfi afj j bij b fi bdj ab² k dfj adi bdf adj adj adfi bdj afij abdi abdf bdf i i bfj abi ab²df ab²df j abij abd abd bdfij b²f fi ab²df ab²df dfj adj abf abf di bfj bdi b²d b²d afj i i j ij abdi abdi abd abd bf abf adi adi aij b²f abdfi abi fj ab² dfj adi adi bfj bdj abi b²f abij ab² bdf ai abdfi abdfj abi abi b afj abf b²d b²d k bfj ak bdk bdi afj i abk abij abfij ij b b abd abd ak abdfj abj ab² bdk b²f adj abd bdij ak b abj abdk bdk bdfi abd k bdf afij bfi dk bk adij abk ab²df dfj k bdj bdj dfk adij j aj b dk bij bfj fij abfi abk j j afi abdk b²f b²f adfk bk adi j abf abf bfj ak dfij ab² ab² abdk i adj b²f adij ab²df ab²df bfi bfi bfj abdk abdfk fi fi bdi ik bdk abf abf bk di abdfj afij afij ik aik k j adfk abdi abfk bfj b²f dik bij dfj j fk fk bfj b²f afi bk abdk bfij bfk adfi adij abi afij bfi ik bdk bdf afk bfj abdfj bdfk ab²df abj afj abij abd b²d ak abdfj jk bdi bfk ik abd abk k ab² ab² aik bfk adfi afk i k ij ij ab²df bfk abd afj b b abik afk bfj bdi abd abd abfij ab² bdjk dk b²d b²d bfj bk abdjk dfj abfi bdj abdfi abdfi bfj aj aj dfj dk bjk adfk ij ij abk bdk dfj afj afj abdj bfj ab² abk ik b adj b²f abdfk ak abdik bdf abfi ik adj adj adk abik abj abj afk bf bf abd k k abdfik abdi fij dfik abdfij adfk dfk dk ab²df ab²df bdj bdik bdk adfk j j abdfik afj b²f b²f abfi adik abk j adj afk ab² abdik afij afij abdk bdjk dj dfi bfik bfik bdfk abdfk bdf j abd afk abdik ak ab²df abj abj di bdfij abdfij abdjk dfk ab²df bdi bdi dfj bjk bjk abk bfik ab² ab²df bfk b abf afik bjk j bdfj ab²df fjk abd bfk afj dfk afi abdjk abdjk abi ajk k afj ai ab² adk dk dfik bdfi bk adik ik fi bdij abik abdik ij aij aj dfj bfk abdjk adfi k adij abdfj afik b aik abd afj k adfk bdik abdfj dfik adj adj dfj bdfjk bj dfij adij fjk abdfij j ijk adfk abjk bj afk b²d dj abdfk afik bjk ijk ijk abj dfik abdfi adj adfjk b b dk fk bdfijk bdijk bdfk j bdf bdf afk b²f b²f bi dfk abk afik di abd adfi afj b²d b²d bdf bdf abfij adj adj bjk abj b²df adjk ik j bdf dijk bfj bdik ab²df ab²df bdk abk bdfjk dfi bfij abdfj abdfj bdi djk ajk abk bdf bdf abfij abfij b²d b²d dfj dfij fik bdik ijk abdi bdfik b²f adfjk afj b b bjk abdjk abdfj b²d b²f bdfijk bdfijk afj bdf afk bik b²d b²d abfi ab²df bfi

Monoid Structure