Details Page for 0.7251

Complete Solution is Known:

MSV File: q-0.7251.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₆₈(0.7251):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,A,B,C,D | a²=1, b³⁰=b²⁸, bc=ab³, c²=b⁴, bd=ab⁵, cd=b⁶, d²=b⁸, b²e=ab⁷, ce=b⁷, de=b⁹, e²=b¹⁰, b³f=b⁹, cf=ab²f, df=ab¹⁰, ef=ab¹¹, f²=b¹², b⁴g=ab¹¹, cg=ab²g, dg=b¹¹, eg=b¹², fg=ab¹³, g²=b¹⁴, b⁵h=b¹³, ch=ab²h, dh=ab⁴h, eh=ab¹³, fh=b¹⁴, gh=ab¹⁵, h²=b¹⁶, b⁶i=ab¹⁵, ci=ab²i, di=ab⁴i, ei=ab⁵i, fi=ab¹⁵, gi=b¹⁶, hi=ab¹⁷, i²=b¹⁸, b⁷j=b¹⁷, cj=ab²j, dj=ab⁴j, ej=ab⁵j, fj=b⁶j, gj=ab¹⁷, hj=b¹⁸, ij=ab¹⁹, j²=b²⁰, b⁸k=ab¹⁹, ck=ab²k, dk=ab⁴k, ek=ab⁵k, fk=b⁶k, gk=ab⁷k, hk=ab¹⁹, ik=b²⁰, jk=ab²¹, k²=b²², b⁹l=b²¹, cl=ab²l, dl=ab⁴l, el=ab⁵l, fl=b⁶l, gl=ab⁷l, hl=b⁸l, il=ab²¹, jl=b²², kl=ab²³, l²=b²⁴, b¹⁰m=ab²³, cm=ab²m, dm=ab⁴m, em=ab⁵m, fm=b⁶m, gm=ab⁷m, hm=b⁸m, im=ab⁹m, jm=ab²³, km=b²⁴, lm=ab²⁵, m²=b²⁶, b¹¹n=b²⁵, cn=ab²n, dn=ab⁴n, en=ab⁵n, fn=b⁶n, gn=ab⁷n, hn=b⁸n, in=ab⁹n, jn=b¹⁰n, kn=ab²⁵, ln=b²⁶, mn=ab²⁷, n²=b²⁸, b¹²o=ab²⁷, co=ab²o, do=ab⁴o, eo=ab⁵o, fo=b⁶o, go=ab⁷o, ho=b⁸o, io=ab⁹o, jo=b¹⁰o, ko=ab¹¹o, lo=ab²⁷, mo=b²⁸, no=ab²⁹, o²=b²⁸, b¹³p=b²⁹, cp=ab²p, dp=ab⁴p, ep=ab⁵p, fp=b⁶p, gp=ab⁷p, hp=b⁸p, ip=ab⁹p, jp=b¹⁰p, kp=ab¹¹p, lp=b¹²p, mp=ab²⁹, np=b²⁸, op=ab²⁹, p²=b²⁸, b¹³q=ab¹²p, cq=ab²q, dq=ab⁴q, eq=ab⁵q, fq=b⁶q, gq=ab⁷q, hq=b⁸q, iq=ab⁹q, jq=b¹⁰q, kq=ab¹¹q, lq=b¹²q, mq=b¹²p, nq=ab²⁹, oq=b²⁸, pq=ab²⁹, q²=b²⁸, b¹²r=ab¹¹q, cr=ab²r, dr=ab⁴r, er=ab⁵r, fr=b⁶r, gr=ab⁷r, hr=b⁸r, ir=ab⁹r, jr=b¹⁰r, kr=ab¹¹r, lr=ab¹¹q, mr=b¹²q, nr=b¹²p, or=ab²⁹, pr=b²⁸, qr=ab²⁹, r²=b²⁸, b¹¹s=ab¹⁰r, cs=ab²s, ds=ab⁴s, es=ab⁵s, fs=b⁶s, gs=ab⁷s, hs=b⁸s, is=ab⁹s, js=b¹⁰s, ks=b¹⁰r, ls=ab¹¹r, ms=ab¹¹q, ns=b¹²q, os=b¹²p, ps=ab²⁹, qs=b²⁸, rs=ab²⁹, s²=b²⁸, b¹⁰t=ab⁹s, ct=ab²t, dt=ab⁴t, et=ab⁵t, ft=b⁶t, gt=ab⁷t, ht=b⁸t, it=ab⁹t, jt=ab⁹s, kt=b¹⁰s, lt=b¹⁰r, mt=ab¹¹r, nt=ab¹¹q, ot=b¹²q, pt=b¹²p, qt=ab²⁹, rt=b²⁸, st=ab²⁹, t²=b²⁸, b⁹u=ab⁸t, cu=ab²u, du=ab⁴u, eu=ab⁵u, fu=b⁶u, gu=ab⁷u, hu=b⁸u, iu=b⁸t, ju=ab⁹t, ku=ab⁹s, lu=b¹⁰s, mu=b¹⁰r, nu=ab¹¹r, ou=ab¹¹q, pu=b¹²q, qu=b¹²p, ru=ab²⁹, su=b²⁸, tu=ab²⁹, u²=b²⁸, b⁸v=ab⁷u, cv=ab²v, dv=ab⁴v, ev=ab⁵v, fv=b⁶v, gv=ab⁷v, hv=ab⁷u, iv=b⁸u, jv=b⁸t, kv=ab⁹t, lv=ab⁹s, mv=b¹⁰s, nv=b¹⁰r, ov=ab¹¹r, pv=ab¹¹q, qv=b¹²q, rv=b¹²p, sv=ab²⁹, tv=b²⁸, uv=ab²⁹, v²=b²⁸, b⁷w=ab⁶v, cw=ab²w, dw=ab⁴w, ew=ab⁵w, fw=b⁶w, gw=b⁶v, hw=ab⁷v, iw=ab⁷u, jw=b⁸u, kw=b⁸t, lw=ab⁹t, mw=ab⁹s, nw=b¹⁰s, ow=b¹⁰r, pw=ab¹¹r, qw=ab¹¹q, rw=b¹²q, sw=b¹²p, tw=ab²⁹, uw=b²⁸, vw=ab²⁹, w²=b²⁸, b⁶x=ab⁵w, cx=ab²x, dx=ab⁴x, ex=ab⁵x, fx=ab⁵w, gx=b⁶w, hx=b⁶v, ix=ab⁷v, jx=ab⁷u, kx=b⁸u, lx=b⁸t, mx=ab⁹t, nx=ab⁹s, ox=b¹⁰s, px=b¹⁰r, qx=ab¹¹r, rx=ab¹¹q, sx=b¹²q, tx=b¹²p, ux=ab²⁹, vx=b²⁸, wx=ab²⁹, x²=b²⁸, b⁵y=ab⁴x, cy=ab²y, dy=ab⁴y, ey=b⁴x, fy=ab⁵x, gy=ab⁵w, hy=b⁶w, iy=b⁶v, jy=ab⁷v, ky=ab⁷u, ly=b⁸u, my=b⁸t, ny=ab⁹t, oy=ab⁹s, py=b¹⁰s, qy=b¹⁰r, ry=ab¹¹r, sy=ab¹¹q, ty=b¹²q, uy=b¹²p, vy=ab²⁹, wy=b²⁸, xy=ab²⁹, y²=b²⁸, b⁴z=ab³y, cz=ab²z, dz=b³y, ez=b⁴y, fz=b⁴x, gz=ab⁵x, hz=ab⁵w, iz=b⁶w, jz=b⁶v, kz=ab⁷v, lz=ab⁷u, mz=b⁸u, nz=b⁸t, oz=ab⁹t, pz=ab⁹s, qz=b¹⁰s, rz=b¹⁰r, sz=ab¹¹r, tz=ab¹¹q, uz=b¹²q, vz=b¹²p, wz=ab²⁹, xz=b²⁸, yz=ab²⁹, z²=b²⁸, b³A=ab²z, cA=ab²A, dA=b³z, eA=ab³y, fA=b⁴y, gA=b⁴x, hA=ab⁵x, iA=ab⁵w, jA=b⁶w, kA=b⁶v, lA=ab⁷v, mA=ab⁷u, nA=b⁸u, oA=b⁸t, pA=ab⁹t, qA=ab⁹s, rA=b¹⁰s, sA=b¹⁰r, tA=ab¹¹r, uA=ab¹¹q, vA=b¹²q, wA=b¹²p, xA=ab²⁹, yA=b²⁸, zA=ab²⁹, A²=b²⁸, b²B=abA, cB=bA, dB=ab²z, eB=ab³z, fB=ab³y, gB=b⁴y, hB=b⁴x, iB=ab⁵x, jB=ab⁵w, kB=b⁶w, lB=b⁶v, mB=ab⁷v, nB=ab⁷u, oB=b⁸u, pB=b⁸t, qB=ab⁹t, rB=ab⁹s, sB=b¹⁰s, tB=b¹⁰r, uB=ab¹¹r, vB=ab¹¹q, wB=b¹²q, xB=b¹²p, yB=ab²⁹, zB=b²⁸, AB=ab²⁹, B²=b²⁸, bC=aB, cC=bB, dC=ab²A, eC=b²z, fC=ab³z, gC=ab³y, hC=b⁴y, iC=b⁴x, jC=ab⁵x, kC=ab⁵w, lC=b⁶w, mC=b⁶v, nC=ab⁷v, oC=ab⁷u, pC=b⁸u, qC=b⁸t, rC=ab⁹t, sC=ab⁹s, tC=b¹⁰s, uC=b¹⁰r, vC=ab¹¹r, wC=ab¹¹q, xC=b¹²q, yC=b¹²p, zC=ab²⁹, AC=b²⁸, BC=ab²⁹, C²=b²⁸, b²D=C, cD=aC, dD=bB, eD=abA, fD=b²A, gD=b²z, hD=ab³z, iD=ab³y, jD=b⁴y, kD=b⁴x, lD=ab⁵x, mD=ab⁵w, nD=b⁶w, oD=b⁶v, pD=ab⁷v, qD=ab⁷u, rD=b⁸u, sD=b⁸t, tD=ab⁹t, uD=ab⁹s, vD=b¹⁰s, wD=b¹⁰r, xD=ab¹¹r, yD=ab¹¹q, zD=b¹²q, AD=b¹²p, BD=ab²⁹, CD=b²⁸, D²=b²⁸>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, b²⁸, e, abf, g, b²g, abh, ab³h, i, b²i, b⁴i, abj, ab³j, ab⁵j, k, b²k, b⁴k, b⁶k, abl, ab³l, ab⁵l, ab⁷l, m, b²m, b⁴m, b⁶m, b⁸m, abn, ab³n, ab⁵n, ab⁷n, ab⁹n, o, b²o, b⁴o, b⁶o, b⁸o, b¹⁰o, abp, ab³p, ab⁵p, ab⁷p, ab⁹p, ab¹¹p, q, b²q, b⁴q, b⁶q, b⁸q, b¹⁰q, b¹²q, abr, ab³r, ab⁵r, ab⁷r, ab⁹r, ab¹¹r, s, b²s, b⁴s, b⁶s, b⁸s, b¹⁰s, abt, ab³t, ab⁵t, ab⁷t, ab⁹t, u, b²u, b⁴u, b⁶u, b⁸u, abv, ab³v, ab⁵v, ab⁷v, w, b²w, b⁴w, b⁶w, abx, ab³x, ab⁵x, y, b²y, b⁴y, abz, ab³z, A, b²A, abB, C, D}

Phi = 1 a 1 b ab a 1 b ab c ac b³ ab³ d ad b⁵ e ab⁶ f b⁷ g ab⁸ h b⁹ i ab¹⁰ j b¹¹ k ab¹² l b¹³ m ab¹⁴ n b¹⁵ o ab¹⁶ p b¹⁷ q ab¹⁸ r b¹⁹ s ab²⁰ t b²¹ u ab²² v b²³ w ab²⁴ x b²⁵ y ab²⁶ z b²⁷ A ab²⁸ B b²⁹ C ab²⁸ abD b²⁹ D ab²⁸

Monoid Structure