Details Page for 0.7143

Complete Solution is Known:

MSV File: q-0.7143.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₈₉(0.7143):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w | a²=1, b²³=b²¹, bc=ab³, c²=b⁴, b²d=ab⁵, cd=b⁵, d²=b⁶, b³e=ab⁷, ce=ab²e, de=b⁷, e²=b⁸, b⁴f=ab⁹, cf=ab²f, df=ab³f, ef=b⁹, f²=b¹⁰, b⁵g=ab¹¹, cg=ab²g, dg=ab³g, eg=ab⁴g, fg=b¹¹, g²=b¹², b⁶h=ab¹³, ch=ab²h, dh=ab³h, eh=ab⁴h, fh=ab⁵h, gh=b¹³, h²=b¹⁴, b⁷i=ab¹⁵, ci=ab²i, di=ab³i, ei=ab⁴i, fi=ab⁵i, gi=ab⁶i, hi=b¹⁵, i²=b¹⁶, b⁸j=ab¹⁷, cj=ab²j, dj=ab³j, ej=ab⁴j, fj=ab⁵j, gj=ab⁶j, hj=ab⁷j, ij=b¹⁷, j²=b¹⁸, b⁹k=ab¹⁹, ck=ab²k, dk=ab³k, ek=ab⁴k, fk=ab⁵k, gk=ab⁶k, hk=ab⁷k, ik=ab⁸k, jk=b¹⁹, k²=b²⁰, b¹⁰l=ab²¹, cl=ab²l, dl=ab³l, el=ab⁴l, fl=ab⁵l, gl=ab⁶l, hl=ab⁷l, il=ab⁸l, jl=ab⁹l, kl=b²¹, l²=b²², b¹¹m=ab²¹, cm=ab²m, dm=ab³m, em=ab⁴m, fm=ab⁵m, gm=ab⁶m, hm=ab⁷m, im=ab⁸m, jm=ab⁹m, km=ab¹⁰m, lm=b²¹, m²=b²², b¹⁰n=b⁹m, cn=ab²n, dn=ab³n, en=ab⁴n, fn=ab⁵n, gn=ab⁶n, hn=ab⁷n, in=ab⁸n, jn=ab⁹n, kn=ab⁹m, ln=ab¹⁰m, mn=b²¹, n²=b²², b⁹o=b⁸n, co=ab²o, do=ab³o, eo=ab⁴o, fo=ab⁵o, go=ab⁶o, ho=ab⁷o, io=ab⁸o, jo=ab⁸n, ko=ab⁹n, lo=ab⁹m, mo=ab¹⁰m, no=b²¹, o²=b²², b⁸p=b⁷o, cp=ab²p, dp=ab³p, ep=ab⁴p, fp=ab⁵p, gp=ab⁶p, hp=ab⁷p, ip=ab⁷o, jp=ab⁸o, kp=ab⁸n, lp=ab⁹n, mp=ab⁹m, np=ab¹⁰m, op=b²¹, p²=b²², b⁷q=b⁶p, cq=ab²q, dq=ab³q, eq=ab⁴q, fq=ab⁵q, gq=ab⁶q, hq=ab⁶p, iq=ab⁷p, jq=ab⁷o, kq=ab⁸o, lq=ab⁸n, mq=ab⁹n, nq=ab⁹m, oq=ab¹⁰m, pq=b²¹, q²=b²², b⁶r=b⁵q, cr=ab²r, dr=ab³r, er=ab⁴r, fr=ab⁵r, gr=ab⁵q, hr=ab⁶q, ir=ab⁶p, jr=ab⁷p, kr=ab⁷o, lr=ab⁸o, mr=ab⁸n, nr=ab⁹n, or=ab⁹m, pr=ab¹⁰m, qr=b²¹, r²=b²², b⁵s=b⁴r, cs=ab²s, ds=ab³s, es=ab⁴s, fs=ab⁴r, gs=ab⁵r, hs=ab⁵q, is=ab⁶q, js=ab⁶p, ks=ab⁷p, ls=ab⁷o, ms=ab⁸o, ns=ab⁸n, os=ab⁹n, ps=ab⁹m, qs=ab¹⁰m, rs=b²¹, s²=b²², b⁴t=b³s, ct=ab²t, dt=ab³t, et=ab³s, ft=ab⁴s, gt=ab⁴r, ht=ab⁵r, it=ab⁵q, jt=ab⁶q, kt=ab⁶p, lt=ab⁷p, mt=ab⁷o, nt=ab⁸o, ot=ab⁸n, pt=ab⁹n, qt=ab⁹m, rt=ab¹⁰m, st=b²¹, t²=b²², b³u=b²t, cu=ab²u, du=ab²t, eu=ab³t, fu=ab³s, gu=ab⁴s, hu=ab⁴r, iu=ab⁵r, ju=ab⁵q, ku=ab⁶q, lu=ab⁶p, mu=ab⁷p, nu=ab⁷o, ou=ab⁸o, pu=ab⁸n, qu=ab⁹n, ru=ab⁹m, su=ab¹⁰m, tu=b²¹, u²=b²², b²v=bu, cv=abu, dv=ab²u, ev=ab²t, fv=ab³t, gv=ab³s, hv=ab⁴s, iv=ab⁴r, jv=ab⁵r, kv=ab⁵q, lv=ab⁶q, mv=ab⁶p, nv=ab⁷p, ov=ab⁷o, pv=ab⁸o, qv=ab⁸n, rv=ab⁹n, sv=ab⁹m, tv=ab¹⁰m, uv=b²¹, v²=b²², bw=v, cw=abv, dw=abu, ew=ab²u, fw=ab²t, gw=ab³t, hw=ab³s, iw=ab⁴s, jw=ab⁴r, kw=ab⁵r, lw=ab⁵q, mw=ab⁶q, nw=ab⁶p, ow=ab⁷p, pw=ab⁷o, qw=ab⁸o, rw=ab⁸n, sw=ab⁹n, tw=ab⁹m, uw=ab¹⁰m, vw=b²¹, w²=b²²>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², ad, abe, af, ab²f, abg, ab³g, ah, ab²h, ab⁴h, abi, ab³i, ab⁵i, aj, ab²j, ab⁴j, ab⁶j, abk, ab³k, ab⁵k, ab⁷k, al, ab²l, ab⁴l, ab⁶l, ab⁸l, abm, ab³m, ab⁵m, ab⁷m, ab⁹m, an, ab²n, ab⁴n, ab⁶n, ab⁸n, abo, ab³o, ab⁵o, ab⁷o, ap, ab²p, ab⁴p, ab⁶p, abq, ab³q, ab⁵q, ar, ab²r, ab⁴r, abs, ab³s, at, ab²t, abu, av}

Phi = 1 a b a b ab b² ab b² c b³ ab² b³ d b⁴ ab³ b⁴ e b⁵ ab⁴ b⁵ f b⁶ ab⁵ b⁶ g b⁷ ab⁶ b⁷ h b⁸ ab⁷ b⁸ i b⁹ ab⁸ b⁹ j b¹⁰ ab⁹ b¹⁰ k b¹¹ ab¹⁰ b¹¹ l b¹² ab¹¹ b¹² m b¹³ ab¹² b¹³ n b¹⁴ ab¹³ b¹⁴ o b¹⁵ ab¹⁴ b¹⁵ p b¹⁶ ab¹⁵ b¹⁶ q b¹⁷ ab¹⁶ b¹⁷ r b¹⁸ ab¹⁷ b¹⁸ s b¹⁹ ab¹⁸ b¹⁹ t b²⁰ ab¹⁹ b²⁰ u b²¹ ab²⁰ b²¹ v b²² ab²¹ b²² w b²¹ ab²² b²¹

Monoid Structure