Details Page for 0.3072

Complete Solution is Known:

MSV File: q-0.3072.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₉₀(0.3072):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u | a²=1, b¹⁹=b¹⁷, b²c=ab⁴, c²=b⁴, b²d=ab⁶, cd=b⁶, d²=b⁸, b²e=b⁷, ce=ab⁷, de=ab⁹, e²=b¹⁰, b²f=ab⁷, ef=abdf, f²=b¹⁰, b²g=bcf, cg=abcf, dg=ab¹⁰, eg=b¹¹, fg=ab¹¹, g²=b¹², b³h=abdf, ch=ab²h, dh=b¹¹, eh=ab¹², fh=b¹², gh=ab¹³, h²=b¹⁴, b⁵i=b¹³, ci=ab²i, di=ab⁴i, ei=b¹³, fi=ab¹³, gi=b¹⁴, hi=ab¹⁵, i²=b¹⁶, b⁶j=ab¹⁵, cj=ab²j, dj=ab⁴j, ej=b⁵j, fj=ab⁵j, gj=ab¹⁵, hj=b¹⁶, ij=ab¹⁷, j²=b¹⁸, b⁷k=b¹⁷, ck=ab²k, dk=ab⁴k, ek=b⁵k, fk=ab⁵k, gk=b⁶k, hk=ab¹⁷, ik=b¹⁸, jk=ab¹⁷, k²=b¹⁸, b⁸l=ab¹⁷, cl=ab²l, dl=ab⁴l, el=b⁵l, fl=ab⁵l, gl=b⁶l, hl=ab⁷l, il=ab¹⁷, jl=b¹⁸, kl=ab¹⁷, l²=b¹⁸, b⁷m=ab⁶l, cm=ab²m, dm=ab⁴m, em=b⁵m, fm=ab⁵m, gm=b⁶m, hm=b⁶l, im=ab⁷l, jm=ab¹⁷, km=b¹⁸, lm=ab¹⁷, m²=b¹⁸, b⁶n=ab⁵m, cn=ab²n, dn=ab⁴n, en=b⁵n, fn=ab⁵n, gn=ab⁵m, hn=b⁶m, in=b⁶l, jn=ab⁷l, kn=ab¹⁷, ln=b¹⁸, mn=ab¹⁷, n²=b¹⁸, b⁵o=ab⁴n, co=ab²o, do=ab⁴o, eo=ab⁴n, fo=b⁴n, go=ab⁵n, ho=ab⁵m, io=b⁶m, jo=b⁶l, ko=ab⁷l, lo=ab¹⁷, mo=b¹⁸, no=ab¹⁷, o²=b¹⁸, b⁴p=ab³o, cp=ab²p, dp=b³o, ep=ab⁴o, fp=b⁴o, gp=b⁴n, hp=ab⁵n, ip=ab⁵m, jp=b⁶m, kp=b⁶l, lp=ab⁷l, mp=ab¹⁷, np=b¹⁸, op=ab¹⁷, p²=b¹⁸, b³q=ab²p, cq=ab²q, dq=b³p, eq=b³o, fq=ab³o, gq=b⁴o, hq=b⁴n, iq=ab⁵n, jq=ab⁵m, kq=b⁶m, lq=b⁶l, mq=ab⁷l, nq=ab¹⁷, oq=b¹⁸, pq=ab¹⁷, q²=b¹⁸, b²r=abq, cr=bq, dr=ab²p, er=b³p, fr=ab³p, gr=ab³o, hr=b⁴o, ir=b⁴n, jr=ab⁵n, kr=ab⁵m, lr=b⁶m, mr=b⁶l, nr=ab⁷l, or=ab¹⁷, pr=b¹⁸, qr=ab¹⁷, r²=b¹⁸, bs=ar, cs=br, ds=ab²q, es=ab²p, fs=b²p, gs=ab³p, hs=ab³o, is=b⁴o, js=b⁴n, ks=ab⁵n, ls=ab⁵m, ms=b⁶m, ns=b⁶l, os=ab⁷l, ps=ab¹⁷, qs=b¹⁸, rs=ab¹⁷, s²=b¹⁸, bt=as, ct=ar, dt=bq, et=ab²q, ft=b²q, gt=b²p, ht=ab³p, it=ab³o, jt=b⁴o, kt=b⁴n, lt=ab⁵n, mt=ab⁵m, nt=b⁶m, ot=b⁶l, pt=ab⁷l, qt=ab¹⁷, rt=b¹⁸, st=ab¹⁷, t²=b¹⁸, bu=at, cu=as, du=br, eu=bq, fu=abq, gu=b²q, hu=b²p, iu=ab³p, ju=ab³o, ku=b⁴o, lu=b⁴n, mu=ab⁵n, nu=ab⁵m, ou=b⁶m, pu=b⁶l, qu=ab⁷l, ru=ab¹⁷, su=b¹⁸, tu=ab¹⁷, u²=b¹⁸>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, ae, bf, abg, h, b²h, abi, ab³i, j, b²j, b⁴j, abk, ab³k, ab⁵k, l, b²l, b⁴l, b⁶l, abm, ab³m, ab⁵m, n, b²n, b⁴n, abo, ab³o, p, b²p, abq, r, t}

Phi = 1 a 1 a 1 b ab b ab a 1 a 1 b ab b ab c ac c b² abc bc abc ab³ d ad d b⁴ e ae e f abe g abe b⁶ bg h bg ab⁷ bh i bh b⁸ bi j bi ab⁹ bj k bj b¹⁰ bk l bk ab¹¹ bl m bl b¹² bm n bm ab¹³ bn o bn b¹⁴ bo p bo ab¹⁵ bp q bp b¹⁶ bq r bq ab¹⁷ br s br b¹⁸ ar t ar ab¹⁷ as u as b¹⁸ at

Monoid Structure