Details Page for 0.7541

Complete Solution is Known:

MSV File: q-0.7541.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₃₈(0.7541):

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, b³²=b³⁰, 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=b³⁰, 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=b³⁰, op=ab³¹, p²=b³⁰, b¹³q=ab³¹, cq=ab²q, dq=ab⁴q, eq=ab⁶q, fq=b⁷q, gq=ab⁸q, hq=b⁹q, iq=ab¹⁰q, jq=b¹¹q, kq=ab¹²q, lq=ab³¹, mq=b³⁰, nq=ab³¹, oq=b³⁰, pq=ab³¹, q²=b³⁰, b¹³r=ab¹²q, cr=ab²r, dr=ab⁴r, er=ab⁶r, fr=b⁷r, gr=ab⁸r, hr=b⁹r, ir=ab¹⁰r, jr=b¹¹r, kr=ab¹²r, lr=ab¹²q, mr=ab³¹, nr=b³⁰, or=ab³¹, pr=b³⁰, qr=ab³¹, r²=b³⁰, b¹²s=ab¹¹r, cs=ab²s, ds=ab⁴s, es=ab⁶s, fs=b⁷s, gs=ab⁸s, hs=b⁹s, is=ab¹⁰s, js=b¹¹s, ks=b¹¹r, ls=ab¹²r, ms=ab¹²q, ns=ab³¹, os=b³⁰, ps=ab³¹, qs=b³⁰, rs=ab³¹, s²=b³⁰, b¹¹t=ab¹⁰s, ct=ab²t, dt=ab⁴t, et=ab⁶t, ft=b⁷t, gt=ab⁸t, ht=b⁹t, it=ab¹⁰t, jt=ab¹⁰s, kt=b¹¹s, lt=b¹¹r, mt=ab¹²r, nt=ab¹²q, ot=ab³¹, pt=b³⁰, qt=ab³¹, rt=b³⁰, st=ab³¹, t²=b³⁰, b¹⁰u=ab⁹t, cu=ab²u, du=ab⁴u, eu=ab⁶u, fu=b⁷u, gu=ab⁸u, hu=b⁹u, iu=b⁹t, ju=ab¹⁰t, ku=ab¹⁰s, lu=b¹¹s, mu=b¹¹r, nu=ab¹²r, ou=ab¹²q, pu=ab³¹, qu=b³⁰, ru=ab³¹, su=b³⁰, tu=ab³¹, u²=b³⁰, b⁹v=ab⁸u, cv=ab²v, dv=ab⁴v, ev=ab⁶v, fv=b⁷v, gv=ab⁸v, hv=ab⁸u, iv=b⁹u, jv=b⁹t, kv=ab¹⁰t, lv=ab¹⁰s, mv=b¹¹s, nv=b¹¹r, ov=ab¹²r, pv=ab¹²q, qv=ab³¹, rv=b³⁰, sv=ab³¹, tv=b³⁰, uv=ab³¹, v²=b³⁰, b⁸w=ab⁷v, cw=ab²w, dw=ab⁴w, ew=ab⁶w, fw=b⁷w, gw=b⁷v, hw=ab⁸v, iw=ab⁸u, jw=b⁹u, kw=b⁹t, lw=ab¹⁰t, mw=ab¹⁰s, nw=b¹¹s, ow=b¹¹r, pw=ab¹²r, qw=ab¹²q, rw=ab³¹, sw=b³⁰, tw=ab³¹, uw=b³⁰, vw=ab³¹, w²=b³⁰, b⁷x=ab⁶w, cx=ab²x, dx=ab⁴x, ex=ab⁶x, fx=ab⁶w, gx=b⁷w, hx=b⁷v, ix=ab⁸v, jx=ab⁸u, kx=b⁹u, lx=b⁹t, mx=ab¹⁰t, nx=ab¹⁰s, ox=b¹¹s, px=b¹¹r, qx=ab¹²r, rx=ab¹²q, sx=ab³¹, tx=b³⁰, ux=ab³¹, vx=b³⁰, wx=ab³¹, x²=b³⁰, b⁶y=ab⁵x, cy=ab²y, dy=ab⁴y, ey=b⁵x, fy=ab⁶x, gy=ab⁶w, hy=b⁷w, iy=b⁷v, jy=ab⁸v, ky=ab⁸u, ly=b⁹u, my=b⁹t, ny=ab¹⁰t, oy=ab¹⁰s, py=b¹¹s, qy=b¹¹r, ry=ab¹²r, sy=ab¹²q, ty=ab³¹, uy=b³⁰, vy=ab³¹, wy=b³⁰, xy=ab³¹, y²=b³⁰, b⁵z=ab⁴y, cz=ab²z, dz=ab⁴z, ez=b⁵y, fz=b⁵x, gz=ab⁶x, hz=ab⁶w, iz=b⁷w, jz=b⁷v, kz=ab⁸v, lz=ab⁸u, mz=b⁹u, nz=b⁹t, oz=ab¹⁰t, pz=ab¹⁰s, qz=b¹¹s, rz=b¹¹r, sz=ab¹²r, tz=ab¹²q, uz=ab³¹, vz=b³⁰, wz=ab³¹, xz=b³⁰, yz=ab³¹, z²=b³⁰, b⁴A=ab³z, cA=ab²A, dA=b³z, eA=ab⁴y, fA=b⁵y, gA=b⁵x, hA=ab⁶x, iA=ab⁶w, jA=b⁷w, kA=b⁷v, lA=ab⁸v, mA=ab⁸u, nA=b⁹u, oA=b⁹t, pA=ab¹⁰t, qA=ab¹⁰s, rA=b¹¹s, sA=b¹¹r, tA=ab¹²r, uA=ab¹²q, vA=ab³¹, wA=b³⁰, xA=ab³¹, yA=b³⁰, zA=ab³¹, A²=b³⁰, b³B=ab²A, cB=ab²B, dB=b³A, eB=ab⁴z, fB=ab⁴y, gB=b⁵y, hB=b⁵x, iB=ab⁶x, jB=ab⁶w, kB=b⁷w, lB=b⁷v, mB=ab⁸v, nB=ab⁸u, oB=b⁹u, pB=b⁹t, qB=ab¹⁰t, rB=ab¹⁰s, sB=b¹¹s, tB=b¹¹r, uB=ab¹²r, vB=ab¹²q, wB=ab³¹, xB=b³⁰, yB=ab³¹, zB=b³⁰, AB=ab³¹, B²=b³⁰, b²C=abB, cC=bB, dC=ab²A, eC=b³z, fC=ab⁴z, gC=ab⁴y, hC=b⁵y, iC=b⁵x, jC=ab⁶x, kC=ab⁶w, lC=b⁷w, mC=b⁷v, nC=ab⁸v, oC=ab⁸u, pC=b⁹u, qC=b⁹t, rC=ab¹⁰t, sC=ab¹⁰s, tC=b¹¹s, uC=b¹¹r, vC=ab¹²r, wC=ab¹²q, xC=ab³¹, yC=b³⁰, zC=ab³¹, AC=b³⁰, BC=ab³¹, C²=b³⁰, bD=aC, cD=bC, dD=ab²B, eD=b³A, fD=b³z, gD=ab⁴z, hD=ab⁴y, iD=b⁵y, jD=b⁵x, kD=ab⁶x, lD=ab⁶w, mD=b⁷w, nD=b⁷v, oD=ab⁸v, pD=ab⁸u, qD=b⁹u, rD=b⁹t, sD=ab¹⁰t, tD=ab¹⁰s, uD=b¹¹s, vD=b¹¹r, wD=ab¹²r, xD=ab¹²q, yD=ab³¹, zD=b³⁰, AD=ab³¹, BD=b³⁰, CD=ab³¹, D²=b³⁰, bE=aD, cE=aC, dE=bB, eE=ab²A, fE=b³A, gE=b³z, hE=ab⁴z, iE=ab⁴y, jE=b⁵y, kE=b⁵x, lE=ab⁶x, mE=ab⁶w, nE=b⁷w, oE=b⁷v, pE=ab⁸v, qE=ab⁸u, rE=b⁹u, sE=b⁹t, tE=ab¹⁰t, uE=ab¹⁰s, vE=b¹¹s, wE=b¹¹r, xE=ab¹²r, yE=ab¹²q, zE=ab³¹, AE=b³⁰, BE=ab³¹, CE=b³⁰, DE=ab³¹, E²=b³⁰, bF=aE, cF=aD, dF=bC, eF=ab²B, fF=ab²A, gF=b³A, hF=b³z, iF=ab⁴z, jF=ab⁴y, kF=b⁵y, lF=b⁵x, mF=ab⁶x, nF=ab⁶w, oF=b⁷w, pF=b⁷v, qF=ab⁸v, rF=ab⁸u, sF=b⁹u, tF=b⁹t, uF=ab¹⁰t, vF=ab¹⁰s, wF=b¹¹s, xF=b¹¹r, yF=ab¹²r, zF=ab¹²q, AF=ab³¹, BF=b³⁰, CF=ab³¹, DF=b³⁰, EF=ab³¹, F²=b³⁰, b²G=F, cG=aF, dG=aD, eG=bC, fG=bB, gG=ab²B, hG=ab²A, iG=b³A, jG=b³z, kG=ab⁴z, lG=ab⁴y, mG=b⁵y, nG=b⁵x, oG=ab⁶x, pG=ab⁶w, qG=b⁷w, rG=b⁷v, sG=ab⁸v, tG=ab⁸u, uG=b⁹u, vG=b⁹t, wG=ab¹⁰t, xG=ab¹⁰s, yG=b¹¹s, zG=b¹¹r, AG=ab¹²r, BG=ab¹²q, CG=ab³¹, DG=b³⁰, EG=ab³¹, FG=b³⁰, G²=b³⁰>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, b²⁸, b³⁰, 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, at, ab²t, ab⁴t, ab⁶t, ab⁸t, ab¹⁰t, bu, b³u, b⁵u, b⁷u, b⁹u, av, ab²v, ab⁴v, ab⁶v, ab⁸v, bw, b³w, b⁵w, b⁷w, ax, ab²x, ab⁴x, ab⁶x, by, b³y, b⁵y, az, ab²z, ab⁴z, bA, b³A, aB, ab²B, bC, aD, aF, aG}

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 abG G

Monoid Structure