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 Q₃₃(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 | a²=1, b²⁷=b²⁵, 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=ab²⁵, m²=b²⁶, b¹⁰n=b²⁵, cn=ab²n, dn=ab⁴n, en=ab⁶n, fn=b⁷n, gn=ab⁸n, hn=b⁹n, in=ab²⁵, jn=b²⁶, kn=ab²⁵, ln=b²⁶, mn=ab²⁵, n²=b²⁶, b¹¹o=ab²⁵, co=ab²o, do=ab⁴o, eo=ab⁶o, fo=b⁷o, go=ab⁸o, ho=b⁹o, io=ab¹⁰o, jo=ab²⁵, ko=b²⁶, lo=ab²⁵, mo=b²⁶, no=ab²⁵, o²=b²⁶, b¹⁰p=ab⁹o, cp=ab²p, dp=ab⁴p, ep=ab⁶p, fp=b⁷p, gp=ab⁸p, hp=b⁹p, ip=b⁹o, jp=ab¹⁰o, kp=ab²⁵, lp=b²⁶, mp=ab²⁵, np=b²⁶, op=ab²⁵, p²=b²⁶, b⁹q=ab⁸p, cq=ab²q, dq=ab⁴q, eq=ab⁶q, fq=b⁷q, gq=ab⁸q, hq=ab⁸p, iq=b⁹p, jq=b⁹o, kq=ab¹⁰o, lq=ab²⁵, mq=b²⁶, nq=ab²⁵, oq=b²⁶, pq=ab²⁵, q²=b²⁶, b⁸r=ab⁷q, cr=ab²r, dr=ab⁴r, er=ab⁶r, fr=b⁷r, gr=b⁷q, hr=ab⁸q, ir=ab⁸p, jr=b⁹p, kr=b⁹o, lr=ab¹⁰o, mr=ab²⁵, nr=b²⁶, or=ab²⁵, pr=b²⁶, qr=ab²⁵, r²=b²⁶, b⁷s=ab⁶r, cs=ab²s, ds=ab⁴s, es=ab⁶s, fs=ab⁶r, gs=b⁷r, hs=b⁷q, is=ab⁸q, js=ab⁸p, ks=b⁹p, ls=b⁹o, ms=ab¹⁰o, ns=ab²⁵, os=b²⁶, ps=ab²⁵, qs=b²⁶, rs=ab²⁵, s²=b²⁶, b⁶t=ab⁵s, ct=ab²t, dt=ab⁴t, et=b⁵s, ft=ab⁶s, gt=ab⁶r, ht=b⁷r, it=b⁷q, jt=ab⁸q, kt=ab⁸p, lt=b⁹p, mt=b⁹o, nt=ab¹⁰o, ot=ab²⁵, pt=b²⁶, qt=ab²⁵, rt=b²⁶, st=ab²⁵, t²=b²⁶, b⁵u=ab⁴t, cu=ab²u, du=ab⁴u, eu=b⁵t, fu=b⁵s, gu=ab⁶s, hu=ab⁶r, iu=b⁷r, ju=b⁷q, ku=ab⁸q, lu=ab⁸p, mu=b⁹p, nu=b⁹o, ou=ab¹⁰o, pu=ab²⁵, qu=b²⁶, ru=ab²⁵, su=b²⁶, tu=ab²⁵, u²=b²⁶, b⁴v=ab³u, cv=ab²v, dv=b³u, ev=ab⁴t, fv=b⁵t, gv=b⁵s, hv=ab⁶s, iv=ab⁶r, jv=b⁷r, kv=b⁷q, lv=ab⁸q, mv=ab⁸p, nv=b⁹p, ov=b⁹o, pv=ab¹⁰o, qv=ab²⁵, rv=b²⁶, sv=ab²⁵, tv=b²⁶, uv=ab²⁵, v²=b²⁶, b³w=ab²v, cw=ab²w, dw=b³v, ew=ab⁴u, fw=ab⁴t, gw=b⁵t, hw=b⁵s, iw=ab⁶s, jw=ab⁶r, kw=b⁷r, lw=b⁷q, mw=ab⁸q, nw=ab⁸p, ow=b⁹p, pw=b⁹o, qw=ab¹⁰o, rw=ab²⁵, sw=b²⁶, tw=ab²⁵, uw=b²⁶, vw=ab²⁵, w²=b²⁶, b²x=abw, cx=bw, dx=ab²v, ex=b³u, fx=ab⁴u, gx=ab⁴t, hx=b⁵t, ix=b⁵s, jx=ab⁶s, kx=ab⁶r, lx=b⁷r, mx=b⁷q, nx=ab⁸q, ox=ab⁸p, px=b⁹p, qx=b⁹o, rx=ab¹⁰o, sx=ab²⁵, tx=b²⁶, ux=ab²⁵, vx=b²⁶, wx=ab²⁵, x²=b²⁶, by=ax, cy=bx, dy=ab²w, ey=b³v, fy=b³u, gy=ab⁴u, hy=ab⁴t, iy=b⁵t, jy=b⁵s, ky=ab⁶s, ly=ab⁶r, my=b⁷r, ny=b⁷q, oy=ab⁸q, py=ab⁸p, qy=b⁹p, ry=b⁹o, sy=ab¹⁰o, ty=ab²⁵, uy=b²⁶, vy=ab²⁵, wy=b²⁶, xy=ab²⁵, y²=b²⁶, bz=ay, cz=ax, dz=bw, ez=ab²v, fz=b³v, gz=b³u, hz=ab⁴u, iz=ab⁴t, jz=b⁵t, kz=b⁵s, lz=ab⁶s, mz=ab⁶r, nz=b⁷r, oz=b⁷q, pz=ab⁸q, qz=ab⁸p, rz=b⁹p, sz=b⁹o, tz=ab¹⁰o, uz=ab²⁵, vz=b²⁶, wz=ab²⁵, xz=b²⁶, yz=ab²⁵, z²=b²⁶, bA=az, cA=ay, dA=bx, eA=ab²w, fA=ab²v, gA=b³v, hA=b³u, iA=ab⁴u, jA=ab⁴t, kA=b⁵t, lA=b⁵s, mA=ab⁶s, nA=ab⁶r, oA=b⁷r, pA=b⁷q, qA=ab⁸q, rA=ab⁸p, sA=b⁹p, tA=b⁹o, uA=ab¹⁰o, vA=ab²⁵, wA=b²⁶, xA=ab²⁵, yA=b²⁶, zA=ab²⁵, A²=b²⁶, bB=aA, cB=az, dB=ax, eB=bw, fB=ab²w, gB=ab²v, hB=b³v, iB=b³u, jB=ab⁴u, kB=ab⁴t, lB=b⁵t, mB=b⁵s, nB=ab⁶s, oB=ab⁶r, pB=b⁷r, qB=b⁷q, rB=ab⁸q, sB=ab⁸p, tB=b⁹p, uB=b⁹o, vB=ab¹⁰o, wB=ab²⁵, xB=b²⁶, yB=ab²⁵, zB=b²⁶, AB=ab²⁵, B²=b²⁶, bC=aB, cC=aA, dC=ay, eC=bx, fC=bw, gC=ab²w, hC=ab²v, iC=b³v, jC=b³u, kC=ab⁴u, lC=ab⁴t, mC=b⁵t, nC=b⁵s, oC=ab⁶s, pC=ab⁶r, qC=b⁷r, rC=b⁷q, sC=ab⁸q, tC=ab⁸p, uC=b⁹p, vC=b⁹o, wC=ab¹⁰o, xC=ab²⁵, yC=b²⁶, zC=ab²⁵, AC=b²⁶, BC=ab²⁵, C²=b²⁶>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, 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, bq, b³q, b⁵q, b⁷q, ar, ab²r, ab⁴r, ab⁶r, bs, b³s, b⁵s, at, ab²t, ab⁴t, bu, b³u, av, ab²v, bw, ax, az, aB}

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

Monoid Structure