Details Page for 0.3271

Complete Solution is Known:

MSV File: q-0.3271.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₆₄(0.3271):

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, b²d=ab⁵, cd=b⁵, d²=b⁶, b³e=b⁷, ce=ab²e, de=ab⁷, e²=b⁸, b⁴f=ab⁹, cf=ab²f, df=ab³f, ef=ab⁹, f²=b¹⁰, b⁵g=b¹¹, cg=ab²g, dg=ab³g, eg=b⁴g, fg=ab¹¹, g²=b¹², b⁶h=ab¹³, ch=ab²h, dh=ab³h, eh=b⁴h, fh=ab⁵h, gh=ab¹³, h²=b¹⁴, b⁷i=b¹⁵, ci=ab²i, di=ab³i, ei=b⁴i, fi=ab⁵i, gi=b⁶i, hi=ab¹⁵, i²=b¹⁶, b⁸j=ab¹⁷, cj=ab²j, dj=ab³j, ej=b⁴j, fj=ab⁵j, gj=b⁶j, hj=ab⁷j, ij=ab¹⁷, j²=b¹⁸, b⁹k=b¹⁹, ck=ab²k, dk=ab³k, ek=b⁴k, fk=ab⁵k, gk=b⁶k, hk=ab⁷k, ik=b⁸k, jk=ab¹⁹, k²=b²⁰, b¹⁰l=ab²¹, cl=ab²l, dl=ab³l, el=b⁴l, fl=ab⁵l, gl=b⁶l, hl=ab⁷l, il=b⁸l, jl=ab⁹l, kl=ab²¹, l²=b²², b¹¹m=b²³, cm=ab²m, dm=ab³m, em=b⁴m, fm=ab⁵m, gm=b⁶m, hm=ab⁷m, im=b⁸m, jm=ab⁹m, km=b¹⁰m, lm=ab²³, m²=b²⁴, b¹²n=ab²⁵, cn=ab²n, dn=ab³n, en=b⁴n, fn=ab⁵n, gn=b⁶n, hn=ab⁷n, in=b⁸n, jn=ab⁹n, kn=b¹⁰n, ln=ab¹¹n, mn=ab²⁵, n²=b²⁶, b¹³o=b²⁷, co=ab²o, do=ab³o, eo=b⁴o, fo=ab⁵o, go=b⁶o, ho=ab⁷o, io=b⁸o, jo=ab⁹o, ko=b¹⁰o, lo=ab¹¹o, mo=b¹²o, no=ab²⁷, o²=b²⁸, b¹⁴p=ab²⁹, cp=ab²p, dp=ab³p, ep=b⁴p, fp=ab⁵p, gp=b⁶p, hp=ab⁷p, ip=b⁸p, jp=ab⁹p, kp=b¹⁰p, lp=ab¹¹p, mp=b¹²p, np=ab¹³p, op=ab²⁹, p²=b²⁸, b¹⁴q=ab¹³p, cq=ab²q, dq=ab³q, eq=b⁴q, fq=ab⁵q, gq=b⁶q, hq=ab⁷q, iq=b⁸q, jq=ab⁹q, kq=b¹⁰q, lq=ab¹¹q, mq=b¹²q, nq=ab¹³q, oq=ab¹³p, pq=ab²⁹, q²=b²⁸, b¹³r=ab¹²q, cr=ab²r, dr=ab³r, er=b⁴r, fr=ab⁵r, gr=b⁶r, hr=ab⁷r, ir=b⁸r, jr=ab⁹r, kr=b¹⁰r, lr=ab¹¹r, mr=b¹²r, nr=b¹²q, or=ab¹³q, pr=ab¹³p, qr=ab²⁹, r²=b²⁸, b¹²s=ab¹¹r, cs=ab²s, ds=ab³s, es=b⁴s, fs=ab⁵s, gs=b⁶s, hs=ab⁷s, is=b⁸s, js=ab⁹s, ks=b¹⁰s, ls=ab¹¹s, ms=ab¹¹r, ns=b¹²r, os=b¹²q, ps=ab¹³q, qs=ab¹³p, rs=ab²⁹, s²=b²⁸, b¹¹t=ab¹⁰s, ct=ab²t, dt=ab³t, et=b⁴t, ft=ab⁵t, gt=b⁶t, ht=ab⁷t, it=b⁸t, jt=ab⁹t, kt=b¹⁰t, lt=b¹⁰s, mt=ab¹¹s, nt=ab¹¹r, ot=b¹²r, pt=b¹²q, qt=ab¹³q, rt=ab¹³p, st=ab²⁹, t²=b²⁸, b¹⁰u=ab⁹t, cu=ab²u, du=ab³u, eu=b⁴u, fu=ab⁵u, gu=b⁶u, hu=ab⁷u, iu=b⁸u, ju=ab⁹u, ku=ab⁹t, lu=b¹⁰t, mu=b¹⁰s, nu=ab¹¹s, ou=ab¹¹r, pu=b¹²r, qu=b¹²q, ru=ab¹³q, su=ab¹³p, tu=ab²⁹, u²=b²⁸, b⁹v=ab⁸u, cv=ab²v, dv=ab³v, ev=b⁴v, fv=ab⁵v, gv=b⁶v, hv=ab⁷v, iv=b⁸v, jv=b⁸u, kv=ab⁹u, lv=ab⁹t, mv=b¹⁰t, nv=b¹⁰s, ov=ab¹¹s, pv=ab¹¹r, qv=b¹²r, rv=b¹²q, sv=ab¹³q, tv=ab¹³p, uv=ab²⁹, v²=b²⁸, b⁸w=ab⁷v, cw=ab²w, dw=ab³w, ew=b⁴w, fw=ab⁵w, gw=b⁶w, hw=ab⁷w, iw=ab⁷v, jw=b⁸v, kw=b⁸u, lw=ab⁹u, mw=ab⁹t, nw=b¹⁰t, ow=b¹⁰s, pw=ab¹¹s, qw=ab¹¹r, rw=b¹²r, sw=b¹²q, tw=ab¹³q, uw=ab¹³p, vw=ab²⁹, w²=b²⁸, b⁷x=ab⁶w, cx=ab²x, dx=ab³x, ex=b⁴x, fx=ab⁵x, gx=b⁶x, hx=b⁶w, ix=ab⁷w, jx=ab⁷v, kx=b⁸v, lx=b⁸u, mx=ab⁹u, nx=ab⁹t, ox=b¹⁰t, px=b¹⁰s, qx=ab¹¹s, rx=ab¹¹r, sx=b¹²r, tx=b¹²q, ux=ab¹³q, vx=ab¹³p, wx=ab²⁹, x²=b²⁸, b⁶y=ab⁵x, cy=ab²y, dy=ab³y, ey=b⁴y, fy=ab⁵y, gy=ab⁵x, hy=b⁶x, iy=b⁶w, jy=ab⁷w, ky=ab⁷v, ly=b⁸v, my=b⁸u, ny=ab⁹u, oy=ab⁹t, py=b¹⁰t, qy=b¹⁰s, ry=ab¹¹s, sy=ab¹¹r, ty=b¹²r, uy=b¹²q, vy=ab¹³q, wy=ab¹³p, xy=ab²⁹, y²=b²⁸, b⁵z=ab⁴y, cz=ab²z, dz=ab³z, ez=b⁴z, fz=b⁴y, gz=ab⁵y, hz=ab⁵x, iz=b⁶x, jz=b⁶w, kz=ab⁷w, lz=ab⁷v, mz=b⁸v, nz=b⁸u, oz=ab⁹u, pz=ab⁹t, qz=b¹⁰t, rz=b¹⁰s, sz=ab¹¹s, tz=ab¹¹r, uz=b¹²r, vz=b¹²q, wz=ab¹³q, xz=ab¹³p, yz=ab²⁹, z²=b²⁸, b⁴A=ab³z, cA=ab²A, dA=ab³A, eA=ab³z, fA=b⁴z, gA=b⁴y, hA=ab⁵y, iA=ab⁵x, jA=b⁶x, kA=b⁶w, lA=ab⁷w, mA=ab⁷v, nA=b⁸v, oA=b⁸u, pA=ab⁹u, qA=ab⁹t, rA=b¹⁰t, sA=b¹⁰s, tA=ab¹¹s, uA=ab¹¹r, vA=b¹²r, wA=b¹²q, xA=ab¹³q, yA=ab¹³p, zA=ab²⁹, A²=b²⁸, b³B=ab²A, cB=ab²B, dB=b²A, eB=ab³A, fB=ab³z, gB=b⁴z, hB=b⁴y, iB=ab⁵y, jB=ab⁵x, kB=b⁶x, lB=b⁶w, mB=ab⁷w, nB=ab⁷v, oB=b⁸v, pB=b⁸u, qB=ab⁹u, rB=ab⁹t, sB=b¹⁰t, tB=b¹⁰s, uB=ab¹¹s, vB=ab¹¹r, wB=b¹²r, xB=b¹²q, yB=ab¹³q, zB=ab¹³p, AB=ab²⁹, B²=b²⁸, b²C=abB, cC=bB, dC=b²B, eC=b²A, fC=ab³A, gC=ab³z, hC=b⁴z, iC=b⁴y, jC=ab⁵y, kC=ab⁵x, lC=b⁶x, mC=b⁶w, nC=ab⁷w, oC=ab⁷v, pC=b⁸v, qC=b⁸u, rC=ab⁹u, sC=ab⁹t, tC=b¹⁰t, uC=b¹⁰s, vC=ab¹¹s, wC=ab¹¹r, xC=b¹²r, yC=b¹²q, zC=ab¹³q, AC=ab¹³p, BC=ab²⁹, C²=b²⁸, bD=aC, cD=bC, dD=abB, eD=b²B, fD=b²A, gD=ab³A, hD=ab³z, iD=b⁴z, jD=b⁴y, kD=ab⁵y, lD=ab⁵x, mD=b⁶x, nD=b⁶w, oD=ab⁷w, pD=ab⁷v, qD=b⁸v, rD=b⁸u, sD=ab⁹u, tD=ab⁹t, uD=b¹⁰t, vD=b¹⁰s, wD=ab¹¹s, xD=ab¹¹r, yD=b¹²r, zD=b¹²q, AD=ab¹³q, BD=ab¹³p, CD=ab²⁹, D²=b²⁸>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, b²⁸, d, abe, f, b²f, abg, ab³g, h, b²h, b⁴h, abi, ab³i, ab⁵i, j, b²j, b⁴j, b⁶j, abk, ab³k, ab⁵k, ab⁷k, l, b²l, b⁴l, b⁶l, b⁸l, abm, ab³m, ab⁵m, ab⁷m, ab⁹m, n, b²n, b⁴n, b⁶n, b⁸n, b¹⁰n, abo, ab³o, ab⁵o, ab⁷o, ab⁹o, ab¹¹o, p, b²p, b⁴p, b⁶p, b⁸p, b¹⁰p, b¹²p, abq, ab³q, ab⁵q, ab⁷q, ab⁹q, ab¹¹q, ab¹³q, r, b²r, b⁴r, b⁶r, b⁸r, b¹⁰r, b¹²r, abs, ab³s, ab⁵s, ab⁷s, ab⁹s, ab¹¹s, t, b²t, b⁴t, b⁶t, b⁸t, b¹⁰t, abu, ab³u, ab⁵u, ab⁷u, ab⁹u, v, b²v, b⁴v, b⁶v, b⁸v, abw, ab³w, ab⁵w, ab⁷w, x, b²x, b⁴x, b⁶x, aby, ab³y, ab⁵y, z, b²z, b⁴z, abA, ab³A, B, b²B, abC, D}

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

Monoid Structure