Details Page for 0.7153

Complete Solution is Known:

MSV File: q-0.7153.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₆₉(0.7153):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r | a²=1, b¹⁸=b¹⁶, 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=b¹⁶, b⁸k=b⁷j, ck=ab²k, dk=ab³k, ek=ab⁴k, fk=ab⁵k, gk=ab⁶k, hk=ab⁷k, ik=ab⁷j, jk=b¹⁷, k²=b¹⁶, b⁷l=b⁶k, cl=ab²l, dl=ab³l, el=ab⁴l, fl=ab⁵l, gl=ab⁶l, hl=ab⁶k, il=ab⁷k, jl=ab⁷j, kl=b¹⁷, l²=b¹⁶, b⁶m=b⁵l, cm=ab²m, dm=ab³m, em=ab⁴m, fm=ab⁵m, gm=ab⁵l, hm=ab⁶l, im=ab⁶k, jm=ab⁷k, km=ab⁷j, lm=b¹⁷, m²=b¹⁶, b⁵n=b⁴m, cn=ab²n, dn=ab³n, en=ab⁴n, fn=ab⁴m, gn=ab⁵m, hn=ab⁵l, in=ab⁶l, jn=ab⁶k, kn=ab⁷k, ln=ab⁷j, mn=b¹⁷, n²=b¹⁶, b⁴o=b³n, co=ab²o, do=ab³o, eo=ab³n, fo=ab⁴n, go=ab⁴m, ho=ab⁵m, io=ab⁵l, jo=ab⁶l, ko=ab⁶k, lo=ab⁷k, mo=ab⁷j, no=b¹⁷, o²=b¹⁶, b³p=b²o, cp=ab²p, dp=ab²o, ep=ab³o, fp=ab³n, gp=ab⁴n, hp=ab⁴m, ip=ab⁵m, jp=ab⁵l, kp=ab⁶l, lp=ab⁶k, mp=ab⁷k, np=ab⁷j, op=b¹⁷, p²=b¹⁶, b²q=bp, cq=abp, dq=ab²p, eq=ab²o, fq=ab³o, gq=ab³n, hq=ab⁴n, iq=ab⁴m, jq=ab⁵m, kq=ab⁵l, lq=ab⁶l, mq=ab⁶k, nq=ab⁷k, oq=ab⁷j, pq=b¹⁷, q²=b¹⁶, br=q, cr=abq, dr=abp, er=ab²p, fr=ab²o, gr=ab³o, hr=ab³n, ir=ab⁴n, jr=ab⁴m, kr=ab⁵m, lr=ab⁵l, mr=ab⁶l, nr=ab⁶k, or=ab⁷k, pr=ab⁷j, qr=b¹⁷, r²=b¹⁶>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, ad, abe, af, ab²f, abg, ab³g, ah, ab²h, ab⁴h, abi, ab³i, ab⁵i, aj, ab²j, ab⁴j, ab⁶j, abk, ab³k, ab⁵k, ab⁷k, al, ab²l, ab⁴l, ab⁶l, abm, ab³m, ab⁵m, an, ab²n, ab⁴n, abo, ab³o, ap, ab²p, abq, ar}

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 b¹⁶ ab¹⁷ b¹⁶

Monoid Structure