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 Q₇₂(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, b³²=b³⁰, 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=b³⁰, 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=b³⁰, op=ab³¹, p²=b³⁰, b¹⁴q=b³¹, cq=ab²q, dq=ab⁴q, eq=b⁵q, fq=ab⁶q, gq=b⁷q, hq=ab⁸q, iq=b⁹q, jq=ab¹⁰q, kq=b¹¹q, lq=ab¹²q, mq=b¹³q, nq=ab³¹, oq=b³⁰, pq=ab³¹, q²=b³⁰, b¹⁴r=ab¹³q, cr=ab²r, dr=ab⁴r, er=b⁵r, fr=ab⁶r, gr=b⁷r, hr=ab⁸r, ir=b⁹r, jr=ab¹⁰r, kr=b¹¹r, lr=ab¹²r, mr=b¹³r, nr=b¹³q, or=ab³¹, pr=b³⁰, qr=ab³¹, r²=b³⁰, b¹³s=ab¹²r, cs=ab²s, ds=ab⁴s, es=b⁵s, fs=ab⁶s, gs=b⁷s, hs=ab⁸s, is=b⁹s, js=ab¹⁰s, ks=b¹¹s, ls=ab¹²s, ms=ab¹²r, ns=b¹³r, os=b¹³q, ps=ab³¹, qs=b³⁰, rs=ab³¹, s²=b³⁰, b¹²t=ab¹¹s, ct=ab²t, dt=ab⁴t, et=b⁵t, ft=ab⁶t, gt=b⁷t, ht=ab⁸t, it=b⁹t, jt=ab¹⁰t, kt=b¹¹t, lt=b¹¹s, mt=ab¹²s, nt=ab¹²r, ot=b¹³r, pt=b¹³q, qt=ab³¹, rt=b³⁰, st=ab³¹, t²=b³⁰, b¹¹u=ab¹⁰t, cu=ab²u, du=ab⁴u, eu=b⁵u, fu=ab⁶u, gu=b⁷u, hu=ab⁸u, iu=b⁹u, ju=ab¹⁰u, ku=ab¹⁰t, lu=b¹¹t, mu=b¹¹s, nu=ab¹²s, ou=ab¹²r, pu=b¹³r, qu=b¹³q, ru=ab³¹, su=b³⁰, tu=ab³¹, u²=b³⁰, b¹⁰v=ab⁹u, cv=ab²v, dv=ab⁴v, ev=b⁵v, fv=ab⁶v, gv=b⁷v, hv=ab⁸v, iv=b⁹v, jv=b⁹u, kv=ab¹⁰u, lv=ab¹⁰t, mv=b¹¹t, nv=b¹¹s, ov=ab¹²s, pv=ab¹²r, qv=b¹³r, rv=b¹³q, sv=ab³¹, tv=b³⁰, uv=ab³¹, v²=b³⁰, b⁹w=ab⁸v, cw=ab²w, dw=ab⁴w, ew=b⁵w, fw=ab⁶w, gw=b⁷w, hw=ab⁸w, iw=ab⁸v, jw=b⁹v, kw=b⁹u, lw=ab¹⁰u, mw=ab¹⁰t, nw=b¹¹t, ow=b¹¹s, pw=ab¹²s, qw=ab¹²r, rw=b¹³r, sw=b¹³q, tw=ab³¹, uw=b³⁰, vw=ab³¹, w²=b³⁰, b⁸x=ab⁷w, cx=ab²x, dx=ab⁴x, ex=b⁵x, fx=ab⁶x, gx=b⁷x, hx=b⁷w, ix=ab⁸w, jx=ab⁸v, kx=b⁹v, lx=b⁹u, mx=ab¹⁰u, nx=ab¹⁰t, ox=b¹¹t, px=b¹¹s, qx=ab¹²s, rx=ab¹²r, sx=b¹³r, tx=b¹³q, ux=ab³¹, vx=b³⁰, wx=ab³¹, x²=b³⁰, b⁷y=ab⁶x, cy=ab²y, dy=ab⁴y, ey=b⁵y, fy=ab⁶y, gy=ab⁶x, hy=b⁷x, iy=b⁷w, jy=ab⁸w, ky=ab⁸v, ly=b⁹v, my=b⁹u, ny=ab¹⁰u, oy=ab¹⁰t, py=b¹¹t, qy=b¹¹s, ry=ab¹²s, sy=ab¹²r, ty=b¹³r, uy=b¹³q, vy=ab³¹, wy=b³⁰, xy=ab³¹, y²=b³⁰, b⁶z=ab⁵y, cz=ab²z, dz=ab⁴z, ez=b⁵z, fz=b⁵y, gz=ab⁶y, hz=ab⁶x, iz=b⁷x, jz=b⁷w, kz=ab⁸w, lz=ab⁸v, mz=b⁹v, nz=b⁹u, oz=ab¹⁰u, pz=ab¹⁰t, qz=b¹¹t, rz=b¹¹s, sz=ab¹²s, tz=ab¹²r, uz=b¹³r, vz=b¹³q, wz=ab³¹, xz=b³⁰, yz=ab³¹, z²=b³⁰, b⁵A=ab⁴z, cA=ab²A, dA=ab⁴A, eA=ab⁴z, fA=b⁵z, gA=b⁵y, hA=ab⁶y, iA=ab⁶x, jA=b⁷x, kA=b⁷w, lA=ab⁸w, mA=ab⁸v, nA=b⁹v, oA=b⁹u, pA=ab¹⁰u, qA=ab¹⁰t, rA=b¹¹t, sA=b¹¹s, tA=ab¹²s, uA=ab¹²r, vA=b¹³r, wA=b¹³q, xA=ab³¹, yA=b³⁰, zA=ab³¹, A²=b³⁰, b⁴B=ab³A, cB=ab²B, dB=b³A, eB=ab⁴A, fB=ab⁴z, gB=b⁵z, hB=b⁵y, iB=ab⁶y, jB=ab⁶x, kB=b⁷x, lB=b⁷w, mB=ab⁸w, nB=ab⁸v, oB=b⁹v, pB=b⁹u, qB=ab¹⁰u, rB=ab¹⁰t, sB=b¹¹t, tB=b¹¹s, uB=ab¹²s, vB=ab¹²r, wB=b¹³r, xB=b¹³q, yB=ab³¹, zB=b³⁰, AB=ab³¹, B²=b³⁰, b³C=ab²B, cC=ab²C, dC=b³B, eC=b³A, fC=ab⁴A, gC=ab⁴z, hC=b⁵z, iC=b⁵y, jC=ab⁶y, kC=ab⁶x, lC=b⁷x, mC=b⁷w, nC=ab⁸w, oC=ab⁸v, pC=b⁹v, qC=b⁹u, rC=ab¹⁰u, sC=ab¹⁰t, tC=b¹¹t, uC=b¹¹s, vC=ab¹²s, wC=ab¹²r, xC=b¹³r, yC=b¹³q, zC=ab³¹, AC=b³⁰, BC=ab³¹, C²=b³⁰, b⁵D=bC, cD=ab²D, dD=ab⁴D, eD=bC, fD=ab²C, gD=ab²B, hD=b³B, iD=b³A, jD=ab⁴A, kD=ab⁴z, lD=b⁵z, mD=b⁵y, nD=ab⁶y, oD=ab⁶x, pD=b⁷x, qD=b⁷w, rD=ab⁸w, sD=ab⁸v, tD=b⁹v, uD=b⁹u, vD=ab¹⁰u, wD=ab¹⁰t, xD=b¹¹t, yD=b¹¹s, zD=ab¹²s, AD=ab¹²r, BD=b¹³r, CD=b¹³q, D²=b³⁰>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, b²⁸, b³⁰, 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, b¹³r, as, ab²s, ab⁴s, ab⁶s, ab⁸s, ab¹⁰s, ab¹²s, bt, b³t, b⁵t, b⁷t, b⁹t, b¹¹t, au, ab²u, ab⁴u, ab⁶u, ab⁸u, ab¹⁰u, bv, b³v, b⁵v, b⁷v, b⁹v, aw, ab²w, ab⁴w, ab⁶w, ab⁸w, bx, b³x, b⁵x, b⁷x, ay, ab²y, ab⁴y, ab⁶y, bz, b³z, b⁵z, aA, ab²A, ab⁴A, bB, b³B, aC, ab²C, aD, ab²D, ab⁴D}

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 ab³⁰ ab³D b³¹ b²D ab³⁰ abD b³¹ D ab³⁰

Monoid Structure