Details Page for 0.7012

Complete Solution is Known:

MSV File: q-0.7012.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₈₈(0.7012):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v | a²=1, b²²=b²⁰, bc=ab³, c²=b⁴, b²d=ab⁵, cd=b⁵, d²=b⁶, b³e=b⁷, ce=ab²e, de=ab⁷, e²=b⁸, b⁴f=ab⁹, cf=ab²f, df=ab³f, ef=ab⁹, f²=b¹⁰, b⁵g=b¹¹, cg=ab²g, dg=ab³g, eg=b⁴g, fg=ab¹¹, g²=b¹², b⁶h=ab¹³, ch=ab²h, dh=ab³h, eh=b⁴h, fh=ab⁵h, gh=ab¹³, h²=b¹⁴, b⁷i=b¹⁵, ci=ab²i, di=ab³i, ei=b⁴i, fi=ab⁵i, gi=b⁶i, hi=ab¹⁵, i²=b¹⁶, b⁸j=ab¹⁷, cj=ab²j, dj=ab³j, ej=b⁴j, fj=ab⁵j, gj=b⁶j, hj=ab⁷j, ij=ab¹⁷, j²=b¹⁸, b⁹k=b¹⁹, ck=ab²k, dk=ab³k, ek=b⁴k, fk=ab⁵k, gk=b⁶k, hk=ab⁷k, ik=b⁸k, jk=ab¹⁹, k²=b²⁰, b¹⁰l=ab²¹, cl=ab²l, dl=ab³l, el=b⁴l, fl=ab⁵l, gl=b⁶l, hl=ab⁷l, il=b⁸l, jl=ab⁹l, kl=ab²¹, l²=b²⁰, b¹⁰m=ab⁹l, cm=ab²m, dm=ab³m, em=b⁴m, fm=ab⁵m, gm=b⁶m, hm=ab⁷m, im=b⁸m, jm=ab⁹m, km=ab⁹l, lm=ab²¹, m²=b²⁰, b⁹n=ab⁸m, cn=ab²n, dn=ab³n, en=b⁴n, fn=ab⁵n, gn=b⁶n, hn=ab⁷n, in=b⁸n, jn=b⁸m, kn=ab⁹m, ln=ab⁹l, mn=ab²¹, n²=b²⁰, b⁸o=ab⁷n, co=ab²o, do=ab³o, eo=b⁴o, fo=ab⁵o, go=b⁶o, ho=ab⁷o, io=ab⁷n, jo=b⁸n, ko=b⁸m, lo=ab⁹m, mo=ab⁹l, no=ab²¹, o²=b²⁰, b⁷p=ab⁶o, cp=ab²p, dp=ab³p, ep=b⁴p, fp=ab⁵p, gp=b⁶p, hp=b⁶o, ip=ab⁷o, jp=ab⁷n, kp=b⁸n, lp=b⁸m, mp=ab⁹m, np=ab⁹l, op=ab²¹, p²=b²⁰, b⁶q=ab⁵p, cq=ab²q, dq=ab³q, eq=b⁴q, fq=ab⁵q, gq=ab⁵p, hq=b⁶p, iq=b⁶o, jq=ab⁷o, kq=ab⁷n, lq=b⁸n, mq=b⁸m, nq=ab⁹m, oq=ab⁹l, pq=ab²¹, q²=b²⁰, b⁵r=ab⁴q, cr=ab²r, dr=ab³r, er=b⁴r, fr=b⁴q, gr=ab⁵q, hr=ab⁵p, ir=b⁶p, jr=b⁶o, kr=ab⁷o, lr=ab⁷n, mr=b⁸n, nr=b⁸m, or=ab⁹m, pr=ab⁹l, qr=ab²¹, r²=b²⁰, b⁴s=ab³r, cs=ab²s, ds=ab³s, es=ab³r, fs=b⁴r, gs=b⁴q, hs=ab⁵q, is=ab⁵p, js=b⁶p, ks=b⁶o, ls=ab⁷o, ms=ab⁷n, ns=b⁸n, os=b⁸m, ps=ab⁹m, qs=ab⁹l, rs=ab²¹, s²=b²⁰, b³t=ab²s, ct=ab²t, dt=b²s, et=ab³s, ft=ab³r, gt=b⁴r, ht=b⁴q, it=ab⁵q, jt=ab⁵p, kt=b⁶p, lt=b⁶o, mt=ab⁷o, nt=ab⁷n, ot=b⁸n, pt=b⁸m, qt=ab⁹m, rt=ab⁹l, st=ab²¹, t²=b²⁰, b²u=abt, cu=bt, du=b²t, eu=b²s, fu=ab³s, gu=ab³r, hu=b⁴r, iu=b⁴q, ju=ab⁵q, ku=ab⁵p, lu=b⁶p, mu=b⁶o, nu=ab⁷o, ou=ab⁷n, pu=b⁸n, qu=b⁸m, ru=ab⁹m, su=ab⁹l, tu=ab²¹, u²=b²⁰, bv=au, cv=bu, dv=abt, ev=b²t, fv=b²s, gv=ab³s, hv=ab³r, iv=b⁴r, jv=b⁴q, kv=ab⁵q, lv=ab⁵p, mv=b⁶p, nv=b⁶o, ov=ab⁷o, pv=ab⁷n, qv=b⁸n, rv=b⁸m, sv=ab⁹m, tv=ab⁹l, uv=ab²¹, v²=b²⁰>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, d, abe, f, b²f, abg, ab³g, h, b²h, b⁴h, abi, ab³i, ab⁵i, j, b²j, b⁴j, b⁶j, abk, ab³k, ab⁵k, ab⁷k, l, b²l, b⁴l, b⁶l, b⁸l, abm, ab³m, ab⁵m, ab⁷m, ab⁹m, n, b²n, b⁴n, b⁶n, b⁸n, abo, ab³o, ab⁵o, ab⁷o, p, b²p, b⁴p, b⁶p, abq, ab³q, ab⁵q, r, b²r, b⁴r, abs, ab³s, t, b²t, abu, v}

Phi = 1 a 1 a 1 b ab b ab a 1 c ac b ab b³ d ab² b² bd e b³ ab³ be f ab⁴ b⁴ bf g b⁵ ab⁵ bg h ab⁶ b⁶ bh i b⁷ ab⁷ bi j ab⁸ b⁸ bj k b⁹ ab⁹ bk l ab¹⁰ b¹⁰ bl m b¹¹ ab¹¹ bm n ab¹² b¹² bn o b¹³ ab¹³ bo p ab¹⁴ b¹⁴ bp q b¹⁵ ab¹⁵ bq r ab¹⁶ b¹⁶ br s b¹⁷ ab¹⁷ bs t ab¹⁸ b¹⁸ bt u b¹⁹ ab¹⁹ bu v ab²⁰ b²⁰ au

Monoid Structure