Details Page for 0.7551

Complete Solution is Known:

MSV File: q-0.7551.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₄₂(0.7551):

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,E,F,G | a²=1, b³⁶=b³⁴, bc=ab³, c²=b⁴, bd=ab⁵, cd=b⁶, d²=b⁸, be=ab⁷, ce=b⁸, de=b¹⁰, e²=b¹², b²f=b⁹, cf=ab⁹, df=ab¹¹, ef=ab¹³, f²=b¹⁴, b³g=ab¹¹, cg=ab²g, dg=b¹², eg=b¹⁴, fg=ab¹⁵, g²=b¹⁶, b⁴h=b¹³, ch=ab²h, dh=ab¹³, eh=ab¹⁵, fh=b¹⁶, gh=ab¹⁷, h²=b¹⁸, b⁵i=ab¹⁵, ci=ab²i, di=ab⁴i, ei=b¹⁶, fi=ab¹⁷, gi=b¹⁸, hi=ab¹⁹, i²=b²⁰, b⁶j=b¹⁷, cj=ab²j, dj=ab⁴j, ej=ab¹⁷, fj=b¹⁸, gj=ab¹⁹, hj=b²⁰, ij=ab²¹, j²=b²², b⁷k=ab¹⁹, ck=ab²k, dk=ab⁴k, ek=ab⁶k, fk=ab¹⁹, gk=b²⁰, hk=ab²¹, ik=b²², jk=ab²³, k²=b²⁴, b⁸l=b²¹, cl=ab²l, dl=ab⁴l, el=ab⁶l, fl=b⁷l, gl=ab²¹, hl=b²², il=ab²³, jl=b²⁴, kl=ab²⁵, l²=b²⁶, b⁹m=ab²³, cm=ab²m, dm=ab⁴m, em=ab⁶m, fm=b⁷m, gm=ab⁸m, hm=ab²³, im=b²⁴, jm=ab²⁵, km=b²⁶, lm=ab²⁷, m²=b²⁸, b¹⁰n=b²⁵, cn=ab²n, dn=ab⁴n, en=ab⁶n, fn=b⁷n, gn=ab⁸n, hn=b⁹n, in=ab²⁵, jn=b²⁶, kn=ab²⁷, ln=b²⁸, mn=ab²⁹, n²=b³⁰, b¹¹o=ab²⁷, co=ab²o, do=ab⁴o, eo=ab⁶o, fo=b⁷o, go=ab⁸o, ho=b⁹o, io=ab¹⁰o, jo=ab²⁷, ko=b²⁸, lo=ab²⁹, mo=b³⁰, no=ab³¹, o²=b³², b¹²p=b²⁹, cp=ab²p, dp=ab⁴p, ep=ab⁶p, fp=b⁷p, gp=ab⁸p, hp=b⁹p, ip=ab¹⁰p, jp=b¹¹p, kp=ab²⁹, lp=b³⁰, mp=ab³¹, np=b³², op=ab³³, p²=b³⁴, b¹³q=ab³¹, cq=ab²q, dq=ab⁴q, eq=ab⁶q, fq=b⁷q, gq=ab⁸q, hq=b⁹q, iq=ab¹⁰q, jq=b¹¹q, kq=ab¹²q, lq=ab³¹, mq=b³², nq=ab³³, oq=b³⁴, pq=ab³⁵, q²=b³⁴, b¹⁴r=b³³, cr=ab²r, dr=ab⁴r, er=ab⁶r, fr=b⁷r, gr=ab⁸r, hr=b⁹r, ir=ab¹⁰r, jr=b¹¹r, kr=ab¹²r, lr=b¹³r, mr=ab³³, nr=b³⁴, or=ab³⁵, pr=b³⁴, qr=ab³⁵, r²=b³⁴, b¹⁵s=ab³⁵, cs=ab²s, ds=ab⁴s, es=ab⁶s, fs=b⁷s, gs=ab⁸s, hs=b⁹s, is=ab¹⁰s, js=b¹¹s, ks=ab¹²s, ls=b¹³s, ms=ab¹⁴s, ns=ab³⁵, os=b³⁴, ps=ab³⁵, qs=b³⁴, rs=ab³⁵, s²=b³⁴, b¹⁵t=ab¹⁴s, ct=ab²t, dt=ab⁴t, et=ab⁶t, ft=b⁷t, gt=ab⁸t, ht=b⁹t, it=ab¹⁰t, jt=b¹¹t, kt=ab¹²t, lt=b¹³t, mt=ab¹⁴t, nt=ab¹⁴s, ot=ab³⁵, pt=b³⁴, qt=ab³⁵, rt=b³⁴, st=ab³⁵, t²=b³⁴, b¹⁴u=ab¹³t, cu=ab²u, du=ab⁴u, eu=ab⁶u, fu=b⁷u, gu=ab⁸u, hu=b⁹u, iu=ab¹⁰u, ju=b¹¹u, ku=ab¹²u, lu=b¹³u, mu=b¹³t, nu=ab¹⁴t, ou=ab¹⁴s, pu=ab³⁵, qu=b³⁴, ru=ab³⁵, su=b³⁴, tu=ab³⁵, u²=b³⁴, b¹³v=ab¹²u, cv=ab²v, dv=ab⁴v, ev=ab⁶v, fv=b⁷v, gv=ab⁸v, hv=b⁹v, iv=ab¹⁰v, jv=b¹¹v, kv=ab¹²v, lv=ab¹²u, mv=b¹³u, nv=b¹³t, ov=ab¹⁴t, pv=ab¹⁴s, qv=ab³⁵, rv=b³⁴, sv=ab³⁵, tv=b³⁴, uv=ab³⁵, v²=b³⁴, b¹²w=ab¹¹v, cw=ab²w, dw=ab⁴w, ew=ab⁶w, fw=b⁷w, gw=ab⁸w, hw=b⁹w, iw=ab¹⁰w, jw=b¹¹w, kw=b¹¹v, lw=ab¹²v, mw=ab¹²u, nw=b¹³u, ow=b¹³t, pw=ab¹⁴t, qw=ab¹⁴s, rw=ab³⁵, sw=b³⁴, tw=ab³⁵, uw=b³⁴, vw=ab³⁵, w²=b³⁴, b¹¹x=ab¹⁰w, cx=ab²x, dx=ab⁴x, ex=ab⁶x, fx=b⁷x, gx=ab⁸x, hx=b⁹x, ix=ab¹⁰x, jx=ab¹⁰w, kx=b¹¹w, lx=b¹¹v, mx=ab¹²v, nx=ab¹²u, ox=b¹³u, px=b¹³t, qx=ab¹⁴t, rx=ab¹⁴s, sx=ab³⁵, tx=b³⁴, ux=ab³⁵, vx=b³⁴, wx=ab³⁵, x²=b³⁴, b¹⁰y=ab⁹x, cy=ab²y, dy=ab⁴y, ey=ab⁶y, fy=b⁷y, gy=ab⁸y, hy=b⁹y, iy=b⁹x, jy=ab¹⁰x, ky=ab¹⁰w, ly=b¹¹w, my=b¹¹v, ny=ab¹²v, oy=ab¹²u, py=b¹³u, qy=b¹³t, ry=ab¹⁴t, sy=ab¹⁴s, ty=ab³⁵, uy=b³⁴, vy=ab³⁵, wy=b³⁴, xy=ab³⁵, y²=b³⁴, b⁹z=ab⁸y, cz=ab²z, dz=ab⁴z, ez=ab⁶z, fz=b⁷z, gz=ab⁸z, hz=ab⁸y, iz=b⁹y, jz=b⁹x, kz=ab¹⁰x, lz=ab¹⁰w, mz=b¹¹w, nz=b¹¹v, oz=ab¹²v, pz=ab¹²u, qz=b¹³u, rz=b¹³t, sz=ab¹⁴t, tz=ab¹⁴s, uz=ab³⁵, vz=b³⁴, wz=ab³⁵, xz=b³⁴, yz=ab³⁵, z²=b³⁴, b⁸A=ab⁷z, cA=ab²A, dA=ab⁴A, eA=ab⁶A, fA=b⁷A, gA=b⁷z, hA=ab⁸z, iA=ab⁸y, jA=b⁹y, kA=b⁹x, lA=ab¹⁰x, mA=ab¹⁰w, nA=b¹¹w, oA=b¹¹v, pA=ab¹²v, qA=ab¹²u, rA=b¹³u, sA=b¹³t, tA=ab¹⁴t, uA=ab¹⁴s, vA=ab³⁵, wA=b³⁴, xA=ab³⁵, yA=b³⁴, zA=ab³⁵, A²=b³⁴, b⁷B=ab⁶A, cB=ab²B, dB=ab⁴B, eB=ab⁶B, fB=ab⁶A, gB=b⁷A, hB=b⁷z, iB=ab⁸z, jB=ab⁸y, kB=b⁹y, lB=b⁹x, mB=ab¹⁰x, nB=ab¹⁰w, oB=b¹¹w, pB=b¹¹v, qB=ab¹²v, rB=ab¹²u, sB=b¹³u, tB=b¹³t, uB=ab¹⁴t, vB=ab¹⁴s, wB=ab³⁵, xB=b³⁴, yB=ab³⁵, zB=b³⁴, AB=ab³⁵, B²=b³⁴, b⁶C=ab⁵B, cC=ab²C, dC=ab⁴C, eC=b⁵B, fC=ab⁶B, gC=ab⁶A, hC=b⁷A, iC=b⁷z, jC=ab⁸z, kC=ab⁸y, lC=b⁹y, mC=b⁹x, nC=ab¹⁰x, oC=ab¹⁰w, pC=b¹¹w, qC=b¹¹v, rC=ab¹²v, sC=ab¹²u, tC=b¹³u, uC=b¹³t, vC=ab¹⁴t, wC=ab¹⁴s, xC=ab³⁵, yC=b³⁴, zC=ab³⁵, AC=b³⁴, BC=ab³⁵, C²=b³⁴, b⁵D=ab⁴C, cD=ab²D, dD=ab⁴D, eD=b⁵C, fD=b⁵B, gD=ab⁶B, hD=ab⁶A, iD=b⁷A, jD=b⁷z, kD=ab⁸z, lD=ab⁸y, mD=b⁹y, nD=b⁹x, oD=ab¹⁰x, pD=ab¹⁰w, qD=b¹¹w, rD=b¹¹v, sD=ab¹²v, tD=ab¹²u, uD=b¹³u, vD=b¹³t, wD=ab¹⁴t, xD=ab¹⁴s, yD=ab³⁵, zD=b³⁴, AD=ab³⁵, BD=b³⁴, CD=ab³⁵, D²=b³⁴, b⁴E=ab³D, cE=ab²E, dE=b³D, eE=ab⁴C, fE=b⁵C, gE=b⁵B, hE=ab⁶B, iE=ab⁶A, jE=b⁷A, kE=b⁷z, lE=ab⁸z, mE=ab⁸y, nE=b⁹y, oE=b⁹x, pE=ab¹⁰x, qE=ab¹⁰w, rE=b¹¹w, sE=b¹¹v, tE=ab¹²v, uE=ab¹²u, vE=b¹³u, wE=b¹³t, xE=ab¹⁴t, yE=ab¹⁴s, zE=ab³⁵, AE=b³⁴, BE=ab³⁵, CE=b³⁴, DE=ab³⁵, E²=b³⁴, b³F=ab²E, cF=ab²F, dF=b³E, eF=ab⁴D, fF=ab⁴C, gF=b⁵C, hF=b⁵B, iF=ab⁶B, jF=ab⁶A, kF=b⁷A, lF=b⁷z, mF=ab⁸z, nF=ab⁸y, oF=b⁹y, pF=b⁹x, qF=ab¹⁰x, rF=ab¹⁰w, sF=b¹¹w, tF=b¹¹v, uF=ab¹²v, vF=ab¹²u, wF=b¹³u, xF=b¹³t, yF=ab¹⁴t, zF=ab¹⁴s, AF=ab³⁵, BF=b³⁴, CF=ab³⁵, DF=b³⁴, EF=ab³⁵, F²=b³⁴, b⁷G=bF, cG=ab²G, dG=ab⁴G, eG=ab⁶G, fG=bF, gG=ab²F, hG=ab²E, iG=b³E, jG=b³D, kG=ab⁴D, lG=ab⁴C, mG=b⁵C, nG=b⁵B, oG=ab⁶B, pG=ab⁶A, qG=b⁷A, rG=b⁷z, sG=ab⁸z, tG=ab⁸y, uG=b⁹y, vG=b⁹x, wG=ab¹⁰x, xG=ab¹⁰w, yG=b¹¹w, zG=b¹¹v, AG=ab¹²v, BG=ab¹²u, CG=b¹³u, DG=b¹³t, EG=ab¹⁴t, FG=ab¹⁴s, G²=b³⁴>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, b²⁸, b³⁰, b³², b³⁴, af, bg, ah, ab²h, bi, b³i, aj, ab²j, ab⁴j, bk, b³k, b⁵k, al, ab²l, ab⁴l, ab⁶l, bm, b³m, b⁵m, b⁷m, an, ab²n, ab⁴n, ab⁶n, ab⁸n, bo, b³o, b⁵o, b⁷o, b⁹o, ap, ab²p, ab⁴p, ab⁶p, ab⁸p, ab¹⁰p, bq, b³q, b⁵q, b⁷q, b⁹q, b¹¹q, ar, ab²r, ab⁴r, ab⁶r, ab⁸r, ab¹⁰r, ab¹²r, bs, b³s, b⁵s, b⁷s, b⁹s, b¹¹s, b¹³s, at, ab²t, ab⁴t, ab⁶t, ab⁸t, ab¹⁰t, ab¹²t, ab¹⁴t, bu, b³u, b⁵u, b⁷u, b⁹u, b¹¹u, b¹³u, av, ab²v, ab⁴v, ab⁶v, ab⁸v, ab¹⁰v, ab¹²v, bw, b³w, b⁵w, b⁷w, b⁹w, b¹¹w, ax, ab²x, ab⁴x, ab⁶x, ab⁸x, ab¹⁰x, by, b³y, b⁵y, b⁷y, b⁹y, az, ab²z, ab⁴z, ab⁶z, ab⁸z, bA, b³A, b⁵A, b⁷A, aB, ab²B, ab⁴B, ab⁶B, bC, b³C, b⁵C, aD, ab²D, ab⁴D, bE, b³E, aF, ab²F, aG, ab²G, ab⁴G, ab⁶G}

Phi = 1 a b a b c b³ d b⁵ 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 E F ab⁵G b⁴G ab³G b²G abG G

Monoid Structure