Details Page for 0.316

Complete Solution is Known:

MSV File: q-0.316.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₃(0.316):

Q = <a,b,c,d,e,f,g,h,i,j,k,l | a²=1, b⁴=b², b²c=b², c²=c, b²d=b³, d²=1, b²e=b³, ce=bc, e³=de², b²f=ab³, bef=ab³, cf²=abcf, e²f²=b², bf³=ab², ef³=abdf², f⁴=def², b²g=b², cg=c, be²g=ae²f, fg=f, bg²=bg, g³=g², beh=b²h, bcfh=bfh, e²fh=ab³h, bf²h=b³h, g²h=gh, ch²=b²h², e²h²=b²h², bfh²=ab²h², f²h²=b²h², bgh²=adefh², egh²=eh², bh³=ab³h², eh³=defh², fh³=b³h², gh³=h³, h⁴=b²h², i=g, bj=abe, cj=abc, ej=ae², f³hj=b²h, h²j=aeh², f²j²=adf²j, j³=adj², b²k=b², bck=abcdf, bfk=abdf², cfk=bcdf, e²fk=ab³, ef²k=bf², f³k=defk, e²gk=bde², efhk=adef²h, bghk=abdfh, eh²k=adefh², fh²k=ab³h², gh²k=adfh², h³k=ab²h², f²jk=adf³j, fhjk=adf²hj, fj²k=adfjk, ck²=b², bek²=bde²k, fk²=abf², bgk²=bf², eg²k²=bdegk, bhk²=b³h, ehk²=de²hk, ghk²=def²h, h²k²=bdh²k, jk²=aek², bk³=be²k, ek³=de²k², g²k³=bdf², hk³=e²hk, k⁴=e²k², b²l=ab², cl=ack, e²l=ae²g², bfl=bdf², ef²l=abf², f³l=ef², g²l=gl, bhl=abhk, efhl=def²h, f²hl=df³h, eh²l=defh², fh²l=b³h², gh²l=dfh², h³l=b²h², ghjl=hjl, fj²l=adfjl, gj²l=j²l, efkl=bdf², f²kl=efk, begkl=abdf², fhkl=df²hk, eghkl=aef²h, h²kl=abdh²k, fjkl=adf²jl, hjkl=adfhjl, ek²l=bdekl, gk²l=bdgkl, k³l=bdk²l, efl²=de²f, egl²=de²g², h²l²=b²h², fjl²=afjl, gjl²=dj²l, hjl²=dhj²l, j²l²=aj²l, bekl²=abdk²l, ehkl²=adhk²l, k²l²=bdkl², bl³=abgl², el³=ade²g², fl³=adfjl, gl³=l³, hl³=hj²l, jl³=adj²l, l⁴=al³>

P = {a, b², c, ad, bcd, ae, ade, ae², ade², bf, abcf, df, acdf, ef, af², adef², df³, ag, adg, aeg, adeg, ae²g, ade²g, ag², adg², aeg², adeg², ae²g², ade²g², bh, ab³h, ach, dh, eh, afh, cdfh, adefh, df²h, af³h, bgh, dgh, egh, b²h², adh², adeh², adgh², ah³, j, dj, afj, df²j, gj, dgj, g²j, dg²j, ahj, dfhj, aghj, aj², adj², dfj², agj², adgj², ag²j², adg²j², dhj², afhj², dghj², ak, ck, adk, aek, ade²k, dfk, agk, adgk, aegk, ag²k, adg²k, aeg²k, achk, dhk, dghk, adh²k, jk, gjk, g²jk, adj²k, ak², adk², aek², ade²k², agk², adgk², ag²k², adg²k², adk³, l, dl, el, del, adfl, aefl, f²l, gl, dgl, egl, degl, adhl, aehl, fhl, adghl, aeghl, dh²l, ajl, adjl, fjl, agjl, adgjl, hjl, j²l, dj²l, adhj²l, kl, dkl, ekl, gkl, dgkl, egkl, ajkl, agjkl, dk²l, al², adl², ael², adel², dfl², af²l², agl², adgl², dhl², afhl², dghl², jl², djl², adkl², aekl², adgkl², jkl², l³, dl³, dkl³}

Phi = 1 a b c d a e f g h g j k l

Monoid Structure