Details Page for 0.7132

Complete Solution is Known:

MSV File: q-0.7132.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₉₀(0.7132):

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=b⁵, cd=ab⁵, d²=b⁶, b³e=b⁷, ce=ab²e, de=b⁷, e²=b⁸, b⁴f=b⁹, cf=ab²f, df=b³f, ef=b⁹, f²=b¹⁰, b⁵g=b¹¹, cg=ab²g, dg=b³g, eg=b⁴g, fg=b¹¹, g²=b¹², b⁶h=b¹³, ch=ab²h, dh=b³h, eh=b⁴h, fh=b⁵h, gh=b¹³, h²=b¹⁴, b⁷i=b¹⁵, ci=ab²i, di=b³i, ei=b⁴i, fi=b⁵i, gi=b⁶i, hi=b¹⁵, i²=b¹⁶, b⁸j=b¹⁷, cj=ab²j, dj=b³j, ej=b⁴j, fj=b⁵j, gj=b⁶j, hj=b⁷j, ij=b¹⁷, j²=b¹⁸, b⁹k=b¹⁹, ck=ab²k, dk=b³k, ek=b⁴k, fk=b⁵k, gk=b⁶k, hk=b⁷k, ik=b⁸k, jk=b¹⁹, k²=b²⁰, b¹⁰l=b²¹, cl=ab²l, dl=b³l, el=b⁴l, fl=b⁵l, gl=b⁶l, hl=b⁷l, il=b⁸l, jl=b⁹l, kl=b²¹, l²=b²⁰, b¹⁰m=b⁹l, cm=ab²m, dm=b³m, em=b⁴m, fm=b⁵m, gm=b⁶m, hm=b⁷m, im=b⁸m, jm=b⁹m, km=b⁹l, lm=b²¹, m²=b²⁰, b⁹n=b⁸m, cn=ab²n, dn=b³n, en=b⁴n, fn=b⁵n, gn=b⁶n, hn=b⁷n, in=b⁸n, jn=b⁸m, kn=b⁹m, ln=b⁹l, mn=b²¹, n²=b²⁰, b⁸o=b⁷n, co=ab²o, do=b³o, eo=b⁴o, fo=b⁵o, go=b⁶o, ho=b⁷o, io=b⁷n, jo=b⁸n, ko=b⁸m, lo=b⁹m, mo=b⁹l, no=b²¹, o²=b²⁰, b⁷p=b⁶o, cp=ab²p, dp=b³p, ep=b⁴p, fp=b⁵p, gp=b⁶p, hp=b⁶o, ip=b⁷o, jp=b⁷n, kp=b⁸n, lp=b⁸m, mp=b⁹m, np=b⁹l, op=b²¹, p²=b²⁰, b⁶q=b⁵p, cq=ab²q, dq=b³q, eq=b⁴q, fq=b⁵q, gq=b⁵p, hq=b⁶p, iq=b⁶o, jq=b⁷o, kq=b⁷n, lq=b⁸n, mq=b⁸m, nq=b⁹m, oq=b⁹l, pq=b²¹, q²=b²⁰, b⁵r=b⁴q, cr=ab²r, dr=b³r, er=b⁴r, fr=b⁴q, gr=b⁵q, hr=b⁵p, ir=b⁶p, jr=b⁶o, kr=b⁷o, lr=b⁷n, mr=b⁸n, nr=b⁸m, or=b⁹m, pr=b⁹l, qr=b²¹, r²=b²⁰, b⁴s=b³r, cs=ab²s, ds=b³s, es=b³r, fs=b⁴r, gs=b⁴q, hs=b⁵q, is=b⁵p, js=b⁶p, ks=b⁶o, ls=b⁷o, ms=b⁷n, ns=b⁸n, os=b⁸m, ps=b⁹m, qs=b⁹l, rs=b²¹, s²=b²⁰, b³t=b²s, ct=ab²t, dt=b²s, et=b³s, ft=b³r, gt=b⁴r, ht=b⁴q, it=b⁵q, jt=b⁵p, kt=b⁶p, lt=b⁶o, mt=b⁷o, nt=b⁷n, ot=b⁸n, pt=b⁸m, qt=b⁹m, rt=b⁹l, st=b²¹, t²=b²⁰, b²u=bt, cu=abt, du=b²t, eu=b²s, fu=b³s, gu=b³r, hu=b⁴r, iu=b⁴q, ju=b⁵q, ku=b⁵p, lu=b⁶p, mu=b⁶o, nu=b⁷o, ou=b⁷n, pu=b⁸n, qu=b⁸m, ru=b⁹m, su=b⁹l, tu=b²¹, u²=b²⁰, bv=u, cv=abu, dv=bt, ev=b²t, fv=b²s, gv=b³s, hv=b³r, iv=b⁴r, jv=b⁴q, kv=b⁵q, lv=b⁵p, mv=b⁶p, nv=b⁶o, ov=b⁷o, pv=b⁷n, qv=b⁸n, rv=b⁸m, sv=b⁹m, tv=b⁹l, uv=b²¹, v²=b²⁰>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, 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 1 ab 1 ab b a b c 1 ab ac ab³ b c d abd b² ad e abe b³ ae f abf b⁴ af g abg b⁵ ag h abh b⁶ ah i abi b⁷ ai j abj b⁸ aj k abk b⁹ ak l abl b¹⁰ al m abm b¹¹ am n abn b¹² an o abo b¹³ ao p abp b¹⁴ ap q abq b¹⁵ aq r abr b¹⁶ ar s abs b¹⁷ as t abt b¹⁸ at u abu b¹⁹ au v au b²⁰ av

Monoid Structure