Details Page for 0.2224

Complete Solution is Known:

MSV File: q-0.2224.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₇₆(0.2224):

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, b³²=b³⁰, bc=ab³, c²=b⁴, bd=ab⁵, cd=b⁶, d²=b⁸, be=ab⁷, ce=b⁸, de=b¹⁰, e²=b¹², b²f=ab⁹, cf=b⁹, df=b¹¹, ef=b¹³, f²=b¹⁴, b³g=ab¹¹, cg=ab²g, dg=b¹², eg=b¹⁴, fg=b¹⁵, g²=b¹⁶, b⁴h=ab¹³, ch=ab²h, dh=b¹³, eh=b¹⁵, fh=b¹⁶, gh=b¹⁷, h²=b¹⁸, b⁵i=ab¹⁵, ci=ab²i, di=ab⁴i, ei=b¹⁶, fi=b¹⁷, gi=b¹⁸, hi=b¹⁹, i²=b²⁰, b⁶j=ab¹⁷, cj=ab²j, dj=ab⁴j, ej=b¹⁷, fj=b¹⁸, gj=b¹⁹, hj=b²⁰, ij=b²¹, j²=b²², b⁷k=ab¹⁹, ck=ab²k, dk=ab⁴k, ek=ab⁶k, fk=b¹⁹, gk=b²⁰, hk=b²¹, ik=b²², jk=b²³, k²=b²⁴, b⁸l=ab²¹, cl=ab²l, dl=ab⁴l, el=ab⁶l, fl=ab⁷l, gl=b²¹, hl=b²², il=b²³, jl=b²⁴, kl=b²⁵, l²=b²⁶, b⁹m=ab²³, cm=ab²m, dm=ab⁴m, em=ab⁶m, fm=ab⁷m, gm=ab⁸m, hm=b²³, im=b²⁴, jm=b²⁵, km=b²⁶, lm=b²⁷, m²=b²⁸, b¹⁰n=ab²⁵, cn=ab²n, dn=ab⁴n, en=ab⁶n, fn=ab⁷n, gn=ab⁸n, hn=ab⁹n, in=b²⁵, jn=b²⁶, kn=b²⁷, ln=b²⁸, mn=b²⁹, n²=b³⁰, b¹¹o=ab²⁷, co=ab²o, do=ab⁴o, eo=ab⁶o, fo=ab⁷o, go=ab⁸o, ho=ab⁹o, io=ab¹⁰o, jo=b²⁷, ko=b²⁸, lo=b²⁹, mo=b³⁰, no=b³¹, o²=b³⁰, b¹²p=ab²⁹, cp=ab²p, dp=ab⁴p, ep=ab⁶p, fp=ab⁷p, gp=ab⁸p, hp=ab⁹p, ip=ab¹⁰p, jp=ab¹¹p, kp=b²⁹, lp=b³⁰, mp=b³¹, np=b³⁰, op=b³¹, p²=b³⁰, b¹³q=ab³¹, cq=ab²q, dq=ab⁴q, eq=ab⁶q, fq=ab⁷q, gq=ab⁸q, hq=ab⁹q, iq=ab¹⁰q, jq=ab¹¹q, kq=ab¹²q, lq=b³¹, mq=b³⁰, nq=b³¹, oq=b³⁰, pq=b³¹, q²=b³⁰, b¹³r=b¹²q, cr=ab²r, dr=ab⁴r, er=ab⁶r, fr=ab⁷r, gr=ab⁸r, hr=ab⁹r, ir=ab¹⁰r, jr=ab¹¹r, kr=ab¹²r, lr=ab¹²q, mr=b³¹, nr=b³⁰, or=b³¹, pr=b³⁰, qr=b³¹, r²=b³⁰, b¹²s=b¹¹r, cs=ab²s, ds=ab⁴s, es=ab⁶s, fs=ab⁷s, gs=ab⁸s, hs=ab⁹s, is=ab¹⁰s, js=ab¹¹s, ks=ab¹¹r, ls=ab¹²r, ms=ab¹²q, ns=b³¹, os=b³⁰, ps=b³¹, qs=b³⁰, rs=b³¹, s²=b³⁰, b¹¹t=b¹⁰s, ct=ab²t, dt=ab⁴t, et=ab⁶t, ft=ab⁷t, gt=ab⁸t, ht=ab⁹t, it=ab¹⁰t, jt=ab¹⁰s, kt=ab¹¹s, lt=ab¹¹r, mt=ab¹²r, nt=ab¹²q, ot=b³¹, pt=b³⁰, qt=b³¹, rt=b³⁰, st=b³¹, t²=b³⁰, b¹⁰u=b⁹t, cu=ab²u, du=ab⁴u, eu=ab⁶u, fu=ab⁷u, gu=ab⁸u, hu=ab⁹u, iu=ab⁹t, ju=ab¹⁰t, ku=ab¹⁰s, lu=ab¹¹s, mu=ab¹¹r, nu=ab¹²r, ou=ab¹²q, pu=b³¹, qu=b³⁰, ru=b³¹, su=b³⁰, tu=b³¹, u²=b³⁰, b⁹v=b⁸u, cv=ab²v, dv=ab⁴v, ev=ab⁶v, fv=ab⁷v, gv=ab⁸v, hv=ab⁸u, iv=ab⁹u, jv=ab⁹t, kv=ab¹⁰t, lv=ab¹⁰s, mv=ab¹¹s, nv=ab¹¹r, ov=ab¹²r, pv=ab¹²q, qv=b³¹, rv=b³⁰, sv=b³¹, tv=b³⁰, uv=b³¹, v²=b³⁰, b⁸w=b⁷v, cw=ab²w, dw=ab⁴w, ew=ab⁶w, fw=ab⁷w, gw=ab⁷v, hw=ab⁸v, iw=ab⁸u, jw=ab⁹u, kw=ab⁹t, lw=ab¹⁰t, mw=ab¹⁰s, nw=ab¹¹s, ow=ab¹¹r, pw=ab¹²r, qw=ab¹²q, rw=b³¹, sw=b³⁰, tw=b³¹, uw=b³⁰, vw=b³¹, w²=b³⁰, b⁷x=b⁶w, cx=ab²x, dx=ab⁴x, ex=ab⁶x, fx=ab⁶w, gx=ab⁷w, hx=ab⁷v, ix=ab⁸v, jx=ab⁸u, kx=ab⁹u, lx=ab⁹t, mx=ab¹⁰t, nx=ab¹⁰s, ox=ab¹¹s, px=ab¹¹r, qx=ab¹²r, rx=ab¹²q, sx=b³¹, tx=b³⁰, ux=b³¹, vx=b³⁰, wx=b³¹, x²=b³⁰, b⁶y=b⁵x, cy=ab²y, dy=ab⁴y, ey=ab⁵x, fy=ab⁶x, gy=ab⁶w, hy=ab⁷w, iy=ab⁷v, jy=ab⁸v, ky=ab⁸u, ly=ab⁹u, my=ab⁹t, ny=ab¹⁰t, oy=ab¹⁰s, py=ab¹¹s, qy=ab¹¹r, ry=ab¹²r, sy=ab¹²q, ty=b³¹, uy=b³⁰, vy=b³¹, wy=b³⁰, xy=b³¹, y²=b³⁰, b⁵z=b⁴y, cz=ab²z, dz=ab⁴z, ez=ab⁵y, fz=ab⁵x, gz=ab⁶x, hz=ab⁶w, iz=ab⁷w, jz=ab⁷v, kz=ab⁸v, lz=ab⁸u, mz=ab⁹u, nz=ab⁹t, oz=ab¹⁰t, pz=ab¹⁰s, qz=ab¹¹s, rz=ab¹¹r, sz=ab¹²r, tz=ab¹²q, uz=b³¹, vz=b³⁰, wz=b³¹, xz=b³⁰, yz=b³¹, z²=b³⁰, b⁴A=b³z, cA=ab²A, dA=ab³z, eA=ab⁴y, fA=ab⁵y, gA=ab⁵x, hA=ab⁶x, iA=ab⁶w, jA=ab⁷w, kA=ab⁷v, lA=ab⁸v, mA=ab⁸u, nA=ab⁹u, oA=ab⁹t, pA=ab¹⁰t, qA=ab¹⁰s, rA=ab¹¹s, sA=ab¹¹r, tA=ab¹²r, uA=ab¹²q, vA=b³¹, wA=b³⁰, xA=b³¹, yA=b³⁰, zA=b³¹, A²=b³⁰, b³B=b²A, cB=ab²B, dB=ab³A, eB=ab⁴z, fB=ab⁴y, gB=ab⁵y, hB=ab⁵x, iB=ab⁶x, jB=ab⁶w, kB=ab⁷w, lB=ab⁷v, mB=ab⁸v, nB=ab⁸u, oB=ab⁹u, pB=ab⁹t, qB=ab¹⁰t, rB=ab¹⁰s, sB=ab¹¹s, tB=ab¹¹r, uB=ab¹²r, vB=ab¹²q, wB=b³¹, xB=b³⁰, yB=b³¹, zB=b³⁰, AB=b³¹, B²=b³⁰, b⁷C=bB, cC=ab²C, dC=ab⁴C, eC=ab⁶C, fC=abB, gC=ab²B, hC=ab²A, iC=ab³A, jC=ab³z, kC=ab⁴z, lC=ab⁴y, mC=ab⁵y, nC=ab⁵x, oC=ab⁶x, pC=ab⁶w, qC=ab⁷w, rC=ab⁷v, sC=ab⁸v, tC=ab⁸u, uC=ab⁹u, vC=ab⁹t, wC=ab¹⁰t, xC=ab¹⁰s, yC=ab¹¹s, zC=ab¹¹r, AC=ab¹²r, BC=ab¹²q, C²=b³⁰>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, b²⁸, b³⁰, af, abg, ah, ab²h, abi, ab³i, aj, ab²j, ab⁴j, abk, ab³k, ab⁵k, al, ab²l, ab⁴l, ab⁶l, abm, ab³m, ab⁵m, ab⁷m, an, ab²n, ab⁴n, ab⁶n, ab⁸n, abo, ab³o, ab⁵o, ab⁷o, ab⁹o, ap, ab²p, ab⁴p, ab⁶p, ab⁸p, ab¹⁰p, abq, ab³q, ab⁵q, ab⁷q, ab⁹q, ab¹¹q, ar, ab²r, ab⁴r, ab⁶r, ab⁸r, ab¹⁰r, ab¹²r, abs, ab³s, ab⁵s, ab⁷s, ab⁹s, ab¹¹s, at, ab²t, ab⁴t, ab⁶t, ab⁸t, ab¹⁰t, abu, ab³u, ab⁵u, ab⁷u, ab⁹u, av, ab²v, ab⁴v, ab⁶v, ab⁸v, abw, ab³w, ab⁵w, ab⁷w, ax, ab²x, ab⁴x, ab⁶x, aby, ab³y, ab⁵y, az, ab²z, ab⁴z, abA, ab³A, aB, ab²B, aC, ab²C, ab⁴C, ab⁶C}

Phi = 1 1 a b ab 1 a b ab 1 c b ab³ b² d b³ ab⁵ b⁴ e b⁵ f b⁶ g b⁷ h b⁸ i b⁹ j b¹⁰ k b¹¹ l b¹² m b¹³ n b¹⁴ o b¹⁵ p b¹⁶ q b¹⁷ r b¹⁸ s b¹⁹ t b²⁰ u b²¹ v b²² w b²³ x b²⁴ y b²⁵ z b²⁶ A b²⁷ B b²⁸ b⁵C b²⁹ b⁴C b³⁰ b³C b³¹ b²C b³⁰ bC b³¹ C b³⁰

Monoid Structure