Details Page for 0.1751

Complete Solution is Known:

MSV File: q-0.1751.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₆₈(0.1751):

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 | a²=1, b³⁰=b²⁸, bc=ab³, c²=b⁴, bd=ab⁵, cd=b⁶, d²=b⁸, b²e=b⁷, ce=ab⁷, de=ab⁹, e²=b¹⁰, b³f=ab⁹, cf=ab²f, df=b¹⁰, ef=ab¹¹, f²=b¹², b⁴g=b¹¹, cg=ab²g, dg=ab¹¹, eg=b¹², fg=ab¹³, g²=b¹⁴, b⁵h=ab¹³, ch=ab²h, dh=ab⁴h, eh=ab¹³, fh=b¹⁴, gh=ab¹⁵, h²=b¹⁶, b⁶i=b¹⁵, ci=ab²i, di=ab⁴i, ei=b⁵i, fi=ab¹⁵, gi=b¹⁶, hi=ab¹⁷, i²=b¹⁸, b⁷j=ab¹⁷, cj=ab²j, dj=ab⁴j, ej=b⁵j, fj=ab⁶j, gj=ab¹⁷, hj=b¹⁸, ij=ab¹⁹, j²=b²⁰, b⁸k=b¹⁹, ck=ab²k, dk=ab⁴k, ek=b⁵k, fk=ab⁶k, gk=b⁷k, hk=ab¹⁹, ik=b²⁰, jk=ab²¹, k²=b²², b⁹l=ab²¹, cl=ab²l, dl=ab⁴l, el=b⁵l, fl=ab⁶l, gl=b⁷l, hl=ab⁸l, il=ab²¹, jl=b²², kl=ab²³, l²=b²⁴, b¹⁰m=b²³, cm=ab²m, dm=ab⁴m, em=b⁵m, fm=ab⁶m, gm=b⁷m, hm=ab⁸m, im=b⁹m, jm=ab²³, km=b²⁴, lm=ab²⁵, m²=b²⁶, b¹¹n=ab²⁵, cn=ab²n, dn=ab⁴n, en=b⁵n, fn=ab⁶n, gn=b⁷n, hn=ab⁸n, in=b⁹n, jn=ab¹⁰n, kn=ab²⁵, ln=b²⁶, mn=ab²⁷, n²=b²⁸, b¹²o=b²⁷, co=ab²o, do=ab⁴o, eo=b⁵o, fo=ab⁶o, go=b⁷o, ho=ab⁸o, io=b⁹o, jo=ab¹⁰o, ko=b¹¹o, lo=ab²⁷, mo=b²⁸, no=ab²⁹, o²=b²⁸, b¹³p=ab²⁹, cp=ab²p, dp=ab⁴p, ep=b⁵p, fp=ab⁶p, gp=b⁷p, hp=ab⁸p, ip=b⁹p, jp=ab¹⁰p, kp=b¹¹p, lp=ab¹²p, mp=ab²⁹, np=b²⁸, op=ab²⁹, p²=b²⁸, b¹³q=ab¹²p, cq=ab²q, dq=ab⁴q, eq=b⁵q, fq=ab⁶q, gq=b⁷q, hq=ab⁸q, iq=b⁹q, jq=ab¹⁰q, kq=b¹¹q, lq=ab¹²q, mq=ab¹²p, nq=ab²⁹, oq=b²⁸, pq=ab²⁹, q²=b²⁸, b¹²r=ab¹¹q, cr=ab²r, dr=ab⁴r, er=b⁵r, fr=ab⁶r, gr=b⁷r, hr=ab⁸r, ir=b⁹r, jr=ab¹⁰r, kr=b¹¹r, lr=b¹¹q, mr=ab¹²q, nr=ab¹²p, or=ab²⁹, pr=b²⁸, qr=ab²⁹, r²=b²⁸, b¹¹s=ab¹⁰r, cs=ab²s, ds=ab⁴s, es=b⁵s, fs=ab⁶s, gs=b⁷s, hs=ab⁸s, is=b⁹s, js=ab¹⁰s, ks=ab¹⁰r, ls=b¹¹r, ms=b¹¹q, ns=ab¹²q, os=ab¹²p, ps=ab²⁹, qs=b²⁸, rs=ab²⁹, s²=b²⁸, b¹⁰t=ab⁹s, ct=ab²t, dt=ab⁴t, et=b⁵t, ft=ab⁶t, gt=b⁷t, ht=ab⁸t, it=b⁹t, jt=b⁹s, kt=ab¹⁰s, lt=ab¹⁰r, mt=b¹¹r, nt=b¹¹q, ot=ab¹²q, pt=ab¹²p, qt=ab²⁹, rt=b²⁸, st=ab²⁹, t²=b²⁸, b⁹u=ab⁸t, cu=ab²u, du=ab⁴u, eu=b⁵u, fu=ab⁶u, gu=b⁷u, hu=ab⁸u, iu=ab⁸t, ju=b⁹t, ku=b⁹s, lu=ab¹⁰s, mu=ab¹⁰r, nu=b¹¹r, ou=b¹¹q, pu=ab¹²q, qu=ab¹²p, ru=ab²⁹, su=b²⁸, tu=ab²⁹, u²=b²⁸, b⁸v=ab⁷u, cv=ab²v, dv=ab⁴v, ev=b⁵v, fv=ab⁶v, gv=b⁷v, hv=b⁷u, iv=ab⁸u, jv=ab⁸t, kv=b⁹t, lv=b⁹s, mv=ab¹⁰s, nv=ab¹⁰r, ov=b¹¹r, pv=b¹¹q, qv=ab¹²q, rv=ab¹²p, sv=ab²⁹, tv=b²⁸, uv=ab²⁹, v²=b²⁸, b⁷w=ab⁶v, cw=ab²w, dw=ab⁴w, ew=b⁵w, fw=ab⁶w, gw=ab⁶v, hw=b⁷v, iw=b⁷u, jw=ab⁸u, kw=ab⁸t, lw=b⁹t, mw=b⁹s, nw=ab¹⁰s, ow=ab¹⁰r, pw=b¹¹r, qw=b¹¹q, rw=ab¹²q, sw=ab¹²p, tw=ab²⁹, uw=b²⁸, vw=ab²⁹, w²=b²⁸, b⁶x=ab⁵w, cx=ab²x, dx=ab⁴x, ex=b⁵x, fx=b⁵w, gx=ab⁶w, hx=ab⁶v, ix=b⁷v, jx=b⁷u, kx=ab⁸u, lx=ab⁸t, mx=b⁹t, nx=b⁹s, ox=ab¹⁰s, px=ab¹⁰r, qx=b¹¹r, rx=b¹¹q, sx=ab¹²q, tx=ab¹²p, ux=ab²⁹, vx=b²⁸, wx=ab²⁹, x²=b²⁸, b⁵y=ab⁴x, cy=ab²y, dy=ab⁴y, ey=ab⁴x, fy=b⁵x, gy=b⁵w, hy=ab⁶w, iy=ab⁶v, jy=b⁷v, ky=b⁷u, ly=ab⁸u, my=ab⁸t, ny=b⁹t, oy=b⁹s, py=ab¹⁰s, qy=ab¹⁰r, ry=b¹¹r, sy=b¹¹q, ty=ab¹²q, uy=ab¹²p, vy=ab²⁹, wy=b²⁸, xy=ab²⁹, y²=b²⁸, b⁴z=ab³y, cz=ab²z, dz=b³y, ez=ab⁴y, fz=ab⁴x, gz=b⁵x, hz=b⁵w, iz=ab⁶w, jz=ab⁶v, kz=b⁷v, lz=b⁷u, mz=ab⁸u, nz=ab⁸t, oz=b⁹t, pz=b⁹s, qz=ab¹⁰s, rz=ab¹⁰r, sz=b¹¹r, tz=b¹¹q, uz=ab¹²q, vz=ab¹²p, wz=ab²⁹, xz=b²⁸, yz=ab²⁹, z²=b²⁸, b³A=ab²z, cA=ab²A, dA=b³z, eA=b³y, fA=ab⁴y, gA=ab⁴x, hA=b⁵x, iA=b⁵w, jA=ab⁶w, kA=ab⁶v, lA=b⁷v, mA=b⁷u, nA=ab⁸u, oA=ab⁸t, pA=b⁹t, qA=b⁹s, rA=ab¹⁰s, sA=ab¹⁰r, tA=b¹¹r, uA=b¹¹q, vA=ab¹²q, wA=ab¹²p, xA=ab²⁹, yA=b²⁸, zA=ab²⁹, A²=b²⁸, b²B=abA, cB=bA, dB=ab²z, eB=b³z, fB=b³y, gB=ab⁴y, hB=ab⁴x, iB=b⁵x, jB=b⁵w, kB=ab⁶w, lB=ab⁶v, mB=b⁷v, nB=b⁷u, oB=ab⁸u, pB=ab⁸t, qB=b⁹t, rB=b⁹s, sB=ab¹⁰s, tB=ab¹⁰r, uB=b¹¹r, vB=b¹¹q, wB=ab¹²q, xB=ab¹²p, yB=ab²⁹, zB=b²⁸, AB=ab²⁹, B²=b²⁸, bC=aB, cC=bB, dC=ab²A, eC=ab²z, fC=b³z, gC=b³y, hC=ab⁴y, iC=ab⁴x, jC=b⁵x, kC=b⁵w, lC=ab⁶w, mC=ab⁶v, nC=b⁷v, oC=b⁷u, pC=ab⁸u, qC=ab⁸t, rC=b⁹t, sC=b⁹s, tC=ab¹⁰s, uC=ab¹⁰r, vC=b¹¹r, wC=b¹¹q, xC=ab¹²q, yC=ab¹²p, zC=ab²⁹, AC=b²⁸, BC=ab²⁹, C²=b²⁸, b²D=C, cD=aC, dD=bB, eD=bA, fD=ab²A, gD=ab²z, hD=b³z, iD=b³y, jD=ab⁴y, kD=ab⁴x, lD=b⁵x, mD=b⁵w, nD=ab⁶w, oD=ab⁶v, pD=b⁷v, qD=b⁷u, rD=ab⁸u, sD=ab⁸t, tD=b⁹t, uD=b⁹s, vD=ab¹⁰s, wD=ab¹⁰r, xD=b¹¹r, yD=b¹¹q, zD=ab¹²q, AD=ab¹²p, BD=ab²⁹, CD=b²⁸, D²=b²⁸>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, b²⁸, ae, bf, ag, ab²g, bh, b³h, ai, ab²i, ab⁴i, bj, b³j, b⁵j, ak, ab²k, ab⁴k, ab⁶k, bl, b³l, b⁵l, b⁷l, am, ab²m, ab⁴m, ab⁶m, ab⁸m, bn, b³n, b⁵n, b⁷n, b⁹n, ao, ab²o, ab⁴o, ab⁶o, ab⁸o, ab¹⁰o, bp, b³p, b⁵p, b⁷p, b⁹p, b¹¹p, aq, ab²q, ab⁴q, ab⁶q, ab⁸q, ab¹⁰q, ab¹²q, br, b³r, b⁵r, b⁷r, b⁹r, b¹¹r, as, ab²s, ab⁴s, ab⁶s, ab⁸s, ab¹⁰s, bt, b³t, b⁵t, b⁷t, b⁹t, au, ab²u, ab⁴u, ab⁶u, ab⁸u, bv, b³v, b⁵v, b⁷v, aw, ab²w, ab⁴w, ab⁶w, bx, b³x, b⁵x, ay, ab²y, ab⁴y, bz, b³z, aA, ab²A, bB, aC, aD}

Phi = 1 a a b b a a b b c c b³ b³ d d b⁵ e ab⁶ f b⁷ g ab⁸ h b⁹ i ab¹⁰ j b¹¹ k ab¹² l b¹³ m ab¹⁴ n b¹⁵ o ab¹⁶ p b¹⁷ q ab¹⁸ r b¹⁹ s ab²⁰ t b²¹ u ab²² v b²³ w ab²⁴ x b²⁵ y ab²⁶ z b²⁷ A ab²⁸ B b²⁹ C ab²⁸ abD b²⁹ D ab²⁸

Monoid Structure