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 Q₄₁(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, b³⁵=b³³, 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=ab³³, 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=ab³³, pr=b³⁴, qr=ab³³, r²=b³⁴, b¹⁵s=ab³³, cs=ab²s, ds=ab⁴s, es=ab⁶s, fs=b⁷s, gs=ab⁸s, hs=b⁹s, is=ab¹⁰s, js=b¹¹s, ks=ab¹²s, ls=b¹³s, ms=ab¹⁴s, ns=ab³³, os=b³⁴, ps=ab³³, qs=b³⁴, rs=ab³³, s²=b³⁴, b¹⁴t=ab¹³s, ct=ab²t, dt=ab⁴t, et=ab⁶t, ft=b⁷t, gt=ab⁸t, ht=b⁹t, it=ab¹⁰t, jt=b¹¹t, kt=ab¹²t, lt=b¹³t, mt=b¹³s, nt=ab¹⁴s, ot=ab³³, pt=b³⁴, qt=ab³³, rt=b³⁴, st=ab³³, t²=b³⁴, b¹³u=ab¹²t, cu=ab²u, du=ab⁴u, eu=ab⁶u, fu=b⁷u, gu=ab⁸u, hu=b⁹u, iu=ab¹⁰u, ju=b¹¹u, ku=ab¹²u, lu=ab¹²t, mu=b¹³t, nu=b¹³s, ou=ab¹⁴s, pu=ab³³, qu=b³⁴, ru=ab³³, su=b³⁴, tu=ab³³, u²=b³⁴, b¹²v=ab¹¹u, cv=ab²v, dv=ab⁴v, ev=ab⁶v, fv=b⁷v, gv=ab⁸v, hv=b⁹v, iv=ab¹⁰v, jv=b¹¹v, kv=b¹¹u, lv=ab¹²u, mv=ab¹²t, nv=b¹³t, ov=b¹³s, pv=ab¹⁴s, qv=ab³³, rv=b³⁴, sv=ab³³, tv=b³⁴, uv=ab³³, v²=b³⁴, b¹¹w=ab¹⁰v, cw=ab²w, dw=ab⁴w, ew=ab⁶w, fw=b⁷w, gw=ab⁸w, hw=b⁹w, iw=ab¹⁰w, jw=ab¹⁰v, kw=b¹¹v, lw=b¹¹u, mw=ab¹²u, nw=ab¹²t, ow=b¹³t, pw=b¹³s, qw=ab¹⁴s, rw=ab³³, sw=b³⁴, tw=ab³³, uw=b³⁴, vw=ab³³, w²=b³⁴, b¹⁰x=ab⁹w, cx=ab²x, dx=ab⁴x, ex=ab⁶x, fx=b⁷x, gx=ab⁸x, hx=b⁹x, ix=b⁹w, jx=ab¹⁰w, kx=ab¹⁰v, lx=b¹¹v, mx=b¹¹u, nx=ab¹²u, ox=ab¹²t, px=b¹³t, qx=b¹³s, rx=ab¹⁴s, sx=ab³³, tx=b³⁴, ux=ab³³, vx=b³⁴, wx=ab³³, x²=b³⁴, b⁹y=ab⁸x, cy=ab²y, dy=ab⁴y, ey=ab⁶y, fy=b⁷y, gy=ab⁸y, hy=ab⁸x, iy=b⁹x, jy=b⁹w, ky=ab¹⁰w, ly=ab¹⁰v, my=b¹¹v, ny=b¹¹u, oy=ab¹²u, py=ab¹²t, qy=b¹³t, ry=b¹³s, sy=ab¹⁴s, ty=ab³³, uy=b³⁴, vy=ab³³, wy=b³⁴, xy=ab³³, y²=b³⁴, b⁸z=ab⁷y, cz=ab²z, dz=ab⁴z, ez=ab⁶z, fz=b⁷z, gz=b⁷y, hz=ab⁸y, iz=ab⁸x, jz=b⁹x, kz=b⁹w, lz=ab¹⁰w, mz=ab¹⁰v, nz=b¹¹v, oz=b¹¹u, pz=ab¹²u, qz=ab¹²t, rz=b¹³t, sz=b¹³s, tz=ab¹⁴s, uz=ab³³, vz=b³⁴, wz=ab³³, xz=b³⁴, yz=ab³³, z²=b³⁴, b⁷A=ab⁶z, cA=ab²A, dA=ab⁴A, eA=ab⁶A, fA=ab⁶z, gA=b⁷z, hA=b⁷y, iA=ab⁸y, jA=ab⁸x, kA=b⁹x, lA=b⁹w, mA=ab¹⁰w, nA=ab¹⁰v, oA=b¹¹v, pA=b¹¹u, qA=ab¹²u, rA=ab¹²t, sA=b¹³t, tA=b¹³s, uA=ab¹⁴s, vA=ab³³, wA=b³⁴, xA=ab³³, yA=b³⁴, zA=ab³³, A²=b³⁴, b⁶B=ab⁵A, cB=ab²B, dB=ab⁴B, eB=b⁵A, fB=ab⁶A, gB=ab⁶z, hB=b⁷z, iB=b⁷y, jB=ab⁸y, kB=ab⁸x, lB=b⁹x, mB=b⁹w, nB=ab¹⁰w, oB=ab¹⁰v, pB=b¹¹v, qB=b¹¹u, rB=ab¹²u, sB=ab¹²t, tB=b¹³t, uB=b¹³s, vB=ab¹⁴s, wB=ab³³, xB=b³⁴, yB=ab³³, zB=b³⁴, AB=ab³³, B²=b³⁴, b⁵C=ab⁴B, cC=ab²C, dC=ab⁴C, eC=b⁵B, fC=b⁵A, gC=ab⁶A, hC=ab⁶z, iC=b⁷z, jC=b⁷y, kC=ab⁸y, lC=ab⁸x, mC=b⁹x, nC=b⁹w, oC=ab¹⁰w, pC=ab¹⁰v, qC=b¹¹v, rC=b¹¹u, sC=ab¹²u, tC=ab¹²t, uC=b¹³t, vC=b¹³s, wC=ab¹⁴s, xC=ab³³, yC=b³⁴, zC=ab³³, AC=b³⁴, BC=ab³³, C²=b³⁴, b⁴D=ab³C, cD=ab²D, dD=b³C, eD=ab⁴B, fD=b⁵B, gD=b⁵A, hD=ab⁶A, iD=ab⁶z, jD=b⁷z, kD=b⁷y, lD=ab⁸y, mD=ab⁸x, nD=b⁹x, oD=b⁹w, pD=ab¹⁰w, qD=ab¹⁰v, rD=b¹¹v, sD=b¹¹u, tD=ab¹²u, uD=ab¹²t, vD=b¹³t, wD=b¹³s, xD=ab¹⁴s, yD=ab³³, zD=b³⁴, AD=ab³³, BD=b³⁴, CD=ab³³, D²=b³⁴, b³E=ab²D, cE=ab²E, dE=b³D, eE=ab⁴C, fE=ab⁴B, gE=b⁵B, hE=b⁵A, iE=ab⁶A, jE=ab⁶z, kE=b⁷z, lE=b⁷y, mE=ab⁸y, nE=ab⁸x, oE=b⁹x, pE=b⁹w, qE=ab¹⁰w, rE=ab¹⁰v, sE=b¹¹v, tE=b¹¹u, uE=ab¹²u, vE=ab¹²t, wE=b¹³t, xE=b¹³s, yE=ab¹⁴s, zE=ab³³, AE=b³⁴, BE=ab³³, CE=b³⁴, DE=ab³³, E²=b³⁴, b²F=abE, cF=bE, dF=ab²D, eF=b³C, fF=ab⁴C, gF=ab⁴B, hF=b⁵B, iF=b⁵A, jF=ab⁶A, kF=ab⁶z, lF=b⁷z, mF=b⁷y, nF=ab⁸y, oF=ab⁸x, pF=b⁹x, qF=b⁹w, rF=ab¹⁰w, sF=ab¹⁰v, tF=b¹¹v, uF=b¹¹u, vF=ab¹²u, wF=ab¹²t, xF=b¹³t, yF=b¹³s, zF=ab¹⁴s, AF=ab³³, BF=b³⁴, CF=ab³³, DF=b³⁴, EF=ab³³, F²=b³⁴, b⁵G=aF, cG=ab²G, dG=ab⁴G, eG=bF, fG=bE, gG=ab²E, hG=ab²D, iG=b³D, jG=b³C, kG=ab⁴C, lG=ab⁴B, mG=b⁵B, nG=b⁵A, oG=ab⁶A, pG=ab⁶z, qG=b⁷z, rG=b⁷y, sG=ab⁸y, tG=ab⁸x, uG=b⁹x, vG=b⁹w, wG=ab¹⁰w, xG=ab¹⁰v, yG=b¹¹v, zG=b¹¹u, AG=ab¹²u, BG=ab¹²t, CG=b¹³t, DG=b¹³s, EG=ab¹⁴s, FG=ab³³, 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, bu, b³u, b⁵u, b⁷u, b⁹u, b¹¹u, av, ab²v, ab⁴v, ab⁶v, ab⁸v, ab¹⁰v, bw, b³w, b⁵w, b⁷w, b⁹w, ax, ab²x, ab⁴x, ab⁶x, ab⁸x, by, b³y, b⁵y, b⁷y, az, ab²z, ab⁴z, ab⁶z, bA, b³A, b⁵A, aB, ab²B, ab⁴B, bC, b³C, aD, ab²D, bE, aF, bG, b³G}

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 b⁴G ab³G b²G abG G

Monoid Structure