Details Page for 0.7123

Complete Solution is Known:

MSV File: q-0.7123.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₈₈(0.7123):

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=b³, c²=b⁴, b²d=b⁵, cd=b⁵, d²=b⁶, b³e=b⁷, ce=b²e, de=b⁷, e²=b⁸, b⁴f=b⁹, cf=b²f, df=b³f, ef=b⁹, f²=b¹⁰, b⁵g=b¹¹, cg=b²g, dg=b³g, eg=b⁴g, fg=b¹¹, g²=b¹², b⁶h=b¹³, ch=b²h, dh=b³h, eh=b⁴h, fh=b⁵h, gh=b¹³, h²=b¹⁴, b⁷i=b¹⁵, ci=b²i, di=b³i, ei=b⁴i, fi=b⁵i, gi=b⁶i, hi=b¹⁵, i²=b¹⁶, b⁸j=b¹⁷, cj=b²j, dj=b³j, ej=b⁴j, fj=b⁵j, gj=b⁶j, hj=b⁷j, ij=b¹⁷, j²=b¹⁸, b⁹k=b¹⁹, ck=b²k, dk=b³k, ek=b⁴k, fk=b⁵k, gk=b⁶k, hk=b⁷k, ik=b⁸k, jk=b¹⁹, k²=b²⁰, b¹⁰l=b²¹, cl=b²l, dl=b³l, el=b⁴l, fl=b⁵l, gl=b⁶l, hl=b⁷l, il=b⁸l, jl=b⁹l, kl=b²¹, l²=b²², b¹¹m=b²¹, cm=b²m, dm=b³m, em=b⁴m, fm=b⁵m, gm=b⁶m, hm=b⁷m, im=b⁸m, jm=b⁹m, km=b¹⁰m, lm=b²¹, m²=b²², b¹⁰n=b⁹m, cn=b²n, dn=b³n, en=b⁴n, fn=b⁵n, gn=b⁶n, hn=b⁷n, in=b⁸n, jn=b⁹n, kn=b⁹m, ln=b¹⁰m, mn=b²¹, n²=b²², b⁹o=b⁸n, co=b²o, do=b³o, eo=b⁴o, fo=b⁵o, go=b⁶o, ho=b⁷o, io=b⁸o, jo=b⁸n, ko=b⁹n, lo=b⁹m, mo=b¹⁰m, no=b²¹, o²=b²², b⁸p=b⁷o, cp=b²p, dp=b³p, ep=b⁴p, fp=b⁵p, gp=b⁶p, hp=b⁷p, ip=b⁷o, jp=b⁸o, kp=b⁸n, lp=b⁹n, mp=b⁹m, np=b¹⁰m, op=b²¹, p²=b²², b⁷q=b⁶p, cq=b²q, dq=b³q, eq=b⁴q, fq=b⁵q, gq=b⁶q, hq=b⁶p, iq=b⁷p, jq=b⁷o, kq=b⁸o, lq=b⁸n, mq=b⁹n, nq=b⁹m, oq=b¹⁰m, pq=b²¹, q²=b²², b⁶r=b⁵q, cr=b²r, dr=b³r, er=b⁴r, fr=b⁵r, gr=b⁵q, hr=b⁶q, ir=b⁶p, jr=b⁷p, kr=b⁷o, lr=b⁸o, mr=b⁸n, nr=b⁹n, or=b⁹m, pr=b¹⁰m, qr=b²¹, r²=b²², b⁵s=b⁴r, cs=b²s, ds=b³s, es=b⁴s, fs=b⁴r, gs=b⁵r, hs=b⁵q, is=b⁶q, js=b⁶p, ks=b⁷p, ls=b⁷o, ms=b⁸o, ns=b⁸n, os=b⁹n, ps=b⁹m, qs=b¹⁰m, rs=b²¹, s²=b²², b⁴t=b³s, ct=b²t, dt=b³t, et=b³s, ft=b⁴s, gt=b⁴r, ht=b⁵r, it=b⁵q, jt=b⁶q, kt=b⁶p, lt=b⁷p, mt=b⁷o, nt=b⁸o, ot=b⁸n, pt=b⁹n, qt=b⁹m, rt=b¹⁰m, st=b²¹, t²=b²², b³u=b²t, cu=b²u, du=b²t, eu=b³t, fu=b³s, gu=b⁴s, hu=b⁴r, iu=b⁵r, ju=b⁵q, ku=b⁶q, lu=b⁶p, mu=b⁷p, nu=b⁷o, ou=b⁸o, pu=b⁸n, qu=b⁹n, ru=b⁹m, su=b¹⁰m, tu=b²¹, u²=b²², b²v=bu, cv=bu, dv=b²u, ev=b²t, fv=b³t, gv=b³s, hv=b⁴s, iv=b⁴r, jv=b⁵r, kv=b⁵q, lv=b⁶q, mv=b⁶p, nv=b⁷p, ov=b⁷o, pv=b⁸o, qv=b⁸n, rv=b⁹n, sv=b⁹m, tv=b¹⁰m, uv=b²¹, v²=b²², bw=v, cw=bv, dw=bu, ew=b²u, fw=b²t, gw=b³t, hw=b³s, iw=b⁴s, jw=b⁴r, kw=b⁵r, lw=b⁵q, mw=b⁶q, nw=b⁶p, ow=b⁷p, pw=b⁷o, qw=b⁸o, rw=b⁸n, sw=b⁹n, tw=b⁹m, uw=b¹⁰m, vw=b²¹, w²=b²²>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², d, be, f, b²f, bg, b³g, h, b²h, b⁴h, bi, b³i, b⁵i, j, b²j, b⁴j, b⁶j, bk, b³k, b⁵k, b⁷k, l, b²l, b⁴l, b⁶l, b⁸l, bm, b³m, b⁵m, b⁷m, b⁹m, n, b²n, b⁴n, b⁶n, b⁸n, bo, b³o, b⁵o, b⁷o, p, b²p, b⁴p, b⁶p, bq, b³q, b⁵q, r, b²r, b⁴r, bs, b³s, t, b²t, bu, v}

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

Monoid Structure