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 Q₃₅(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 | a²=1, b²⁹=b²⁷, 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=ab²⁷, n²=b²⁸, b¹¹o=ab²⁷, co=ab²o, do=ab⁴o, eo=ab⁶o, fo=b⁷o, go=ab⁸o, ho=b⁹o, io=ab¹⁰o, jo=ab²⁷, ko=b²⁸, lo=ab²⁷, mo=b²⁸, no=ab²⁷, o²=b²⁸, b¹²p=b²⁷, cp=ab²p, dp=ab⁴p, ep=ab⁶p, fp=b⁷p, gp=ab⁸p, hp=b⁹p, ip=ab¹⁰p, jp=b¹¹p, kp=ab²⁷, lp=b²⁸, mp=ab²⁷, np=b²⁸, op=ab²⁷, p²=b²⁸, b¹¹q=ab¹⁰p, cq=ab²q, dq=ab⁴q, eq=ab⁶q, fq=b⁷q, gq=ab⁸q, hq=b⁹q, iq=ab¹⁰q, jq=ab¹⁰p, kq=b¹¹p, lq=ab²⁷, mq=b²⁸, nq=ab²⁷, oq=b²⁸, pq=ab²⁷, q²=b²⁸, b¹⁰r=ab⁹q, cr=ab²r, dr=ab⁴r, er=ab⁶r, fr=b⁷r, gr=ab⁸r, hr=b⁹r, ir=b⁹q, jr=ab¹⁰q, kr=ab¹⁰p, lr=b¹¹p, mr=ab²⁷, nr=b²⁸, or=ab²⁷, pr=b²⁸, qr=ab²⁷, r²=b²⁸, b⁹s=ab⁸r, cs=ab²s, ds=ab⁴s, es=ab⁶s, fs=b⁷s, gs=ab⁸s, hs=ab⁸r, is=b⁹r, js=b⁹q, ks=ab¹⁰q, ls=ab¹⁰p, ms=b¹¹p, ns=ab²⁷, os=b²⁸, ps=ab²⁷, qs=b²⁸, rs=ab²⁷, s²=b²⁸, b⁸t=ab⁷s, ct=ab²t, dt=ab⁴t, et=ab⁶t, ft=b⁷t, gt=b⁷s, ht=ab⁸s, it=ab⁸r, jt=b⁹r, kt=b⁹q, lt=ab¹⁰q, mt=ab¹⁰p, nt=b¹¹p, ot=ab²⁷, pt=b²⁸, qt=ab²⁷, rt=b²⁸, st=ab²⁷, t²=b²⁸, b⁷u=ab⁶t, cu=ab²u, du=ab⁴u, eu=ab⁶u, fu=ab⁶t, gu=b⁷t, hu=b⁷s, iu=ab⁸s, ju=ab⁸r, ku=b⁹r, lu=b⁹q, mu=ab¹⁰q, nu=ab¹⁰p, ou=b¹¹p, pu=ab²⁷, qu=b²⁸, ru=ab²⁷, su=b²⁸, tu=ab²⁷, u²=b²⁸, b⁶v=ab⁵u, cv=ab²v, dv=ab⁴v, ev=b⁵u, fv=ab⁶u, gv=ab⁶t, hv=b⁷t, iv=b⁷s, jv=ab⁸s, kv=ab⁸r, lv=b⁹r, mv=b⁹q, nv=ab¹⁰q, ov=ab¹⁰p, pv=b¹¹p, qv=ab²⁷, rv=b²⁸, sv=ab²⁷, tv=b²⁸, uv=ab²⁷, v²=b²⁸, b⁵w=ab⁴v, cw=ab²w, dw=ab⁴w, ew=b⁵v, fw=b⁵u, gw=ab⁶u, hw=ab⁶t, iw=b⁷t, jw=b⁷s, kw=ab⁸s, lw=ab⁸r, mw=b⁹r, nw=b⁹q, ow=ab¹⁰q, pw=ab¹⁰p, qw=b¹¹p, rw=ab²⁷, sw=b²⁸, tw=ab²⁷, uw=b²⁸, vw=ab²⁷, w²=b²⁸, b⁴x=ab³w, cx=ab²x, dx=b³w, ex=ab⁴v, fx=b⁵v, gx=b⁵u, hx=ab⁶u, ix=ab⁶t, jx=b⁷t, kx=b⁷s, lx=ab⁸s, mx=ab⁸r, nx=b⁹r, ox=b⁹q, px=ab¹⁰q, qx=ab¹⁰p, rx=b¹¹p, sx=ab²⁷, tx=b²⁸, ux=ab²⁷, vx=b²⁸, wx=ab²⁷, x²=b²⁸, b³y=ab²x, cy=ab²y, dy=b³x, ey=ab⁴w, fy=ab⁴v, gy=b⁵v, hy=b⁵u, iy=ab⁶u, jy=ab⁶t, ky=b⁷t, ly=b⁷s, my=ab⁸s, ny=ab⁸r, oy=b⁹r, py=b⁹q, qy=ab¹⁰q, ry=ab¹⁰p, sy=b¹¹p, ty=ab²⁷, uy=b²⁸, vy=ab²⁷, wy=b²⁸, xy=ab²⁷, y²=b²⁸, b²z=aby, cz=by, dz=ab²x, ez=b³w, fz=ab⁴w, gz=ab⁴v, hz=b⁵v, iz=b⁵u, jz=ab⁶u, kz=ab⁶t, lz=b⁷t, mz=b⁷s, nz=ab⁸s, oz=ab⁸r, pz=b⁹r, qz=b⁹q, rz=ab¹⁰q, sz=ab¹⁰p, tz=b¹¹p, uz=ab²⁷, vz=b²⁸, wz=ab²⁷, xz=b²⁸, yz=ab²⁷, z²=b²⁸, bA=az, cA=bz, dA=ab²y, eA=b³x, fA=b³w, gA=ab⁴w, hA=ab⁴v, iA=b⁵v, jA=b⁵u, kA=ab⁶u, lA=ab⁶t, mA=b⁷t, nA=b⁷s, oA=ab⁸s, pA=ab⁸r, qA=b⁹r, rA=b⁹q, sA=ab¹⁰q, tA=ab¹⁰p, uA=b¹¹p, vA=ab²⁷, wA=b²⁸, xA=ab²⁷, yA=b²⁸, zA=ab²⁷, A²=b²⁸, bB=aA, cB=az, dB=by, eB=ab²x, fB=b³x, gB=b³w, hB=ab⁴w, iB=ab⁴v, jB=b⁵v, kB=b⁵u, lB=ab⁶u, mB=ab⁶t, nB=b⁷t, oB=b⁷s, pB=ab⁸s, qB=ab⁸r, rB=b⁹r, sB=b⁹q, tB=ab¹⁰q, uB=ab¹⁰p, vB=b¹¹p, wB=ab²⁷, xB=b²⁸, yB=ab²⁷, zB=b²⁸, AB=ab²⁷, B²=b²⁸, bC=aB, cC=aA, dC=bz, eC=ab²y, fC=ab²x, gC=b³x, hC=b³w, iC=ab⁴w, jC=ab⁴v, kC=b⁵v, lC=b⁵u, mC=ab⁶u, nC=ab⁶t, oC=b⁷t, pC=b⁷s, qC=ab⁸s, rC=ab⁸r, sC=b⁹r, tC=b⁹q, uC=ab¹⁰q, vC=ab¹⁰p, wC=b¹¹p, xC=ab²⁷, yC=b²⁸, zC=ab²⁷, AC=b²⁸, BC=ab²⁷, C²=b²⁸, bD=aC, cD=aB, dD=az, eD=by, fD=ab²y, gD=ab²x, hD=b³x, iD=b³w, jD=ab⁴w, kD=ab⁴v, lD=b⁵v, mD=b⁵u, nD=ab⁶u, oD=ab⁶t, pD=b⁷t, qD=b⁷s, rD=ab⁸s, sD=ab⁸r, tD=b⁹r, uD=b⁹q, vD=ab¹⁰q, wD=ab¹⁰p, xD=b¹¹p, yD=ab²⁷, zD=b²⁸, AD=ab²⁷, BD=b²⁸, CD=ab²⁷, D²=b²⁸, bE=aD, cE=aC, dE=aA, eE=bz, fE=by, gE=ab²y, hE=ab²x, iE=b³x, jE=b³w, kE=ab⁴w, lE=ab⁴v, mE=b⁵v, nE=b⁵u, oE=ab⁶u, pE=ab⁶t, qE=b⁷t, rE=b⁷s, sE=ab⁸s, tE=ab⁸r, uE=b⁹r, vE=b⁹q, wE=ab¹⁰q, xE=ab¹⁰p, yE=b¹¹p, zE=ab²⁷, AE=b²⁸, BE=ab²⁷, CE=b²⁸, DE=ab²⁷, E²=b²⁸>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, b²⁸, 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, ar, ab²r, ab⁴r, ab⁶r, ab⁸r, bs, b³s, b⁵s, b⁷s, at, ab²t, ab⁴t, ab⁶t, bu, b³u, b⁵u, av, ab²v, ab⁴v, bw, b³w, ax, ab²x, by, az, aB, aD}

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

Monoid Structure