Details Page for 0.3551

Complete Solution is Known:

MSV File: q-0.3551.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₄₄(0.3551):

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,E,F,G | a²=1, b³⁴=b³², bc=ab³, c²=b⁴, bd=ab⁵, cd=b⁶, d²=b⁸, be=ab⁷, ce=b⁸, de=b¹⁰, e²=b¹², bf=ab⁹, cf=b¹⁰, df=b¹², ef=b¹⁴, f²=b¹⁶, b²g=b¹¹, cg=ab¹¹, dg=ab¹³, eg=ab¹⁵, fg=ab¹⁷, g²=b¹⁸, b³h=ab¹³, ch=ab²h, dh=b¹⁴, eh=b¹⁶, fh=b¹⁸, gh=ab¹⁹, h²=b²⁰, b⁴i=b¹⁵, ci=ab²i, di=ab¹⁵, ei=ab¹⁷, fi=ab¹⁹, gi=b²⁰, hi=ab²¹, i²=b²², b⁵j=ab¹⁷, cj=ab²j, dj=ab⁴j, ej=b¹⁸, fj=b²⁰, gj=ab²¹, hj=b²², ij=ab²³, j²=b²⁴, b⁶k=b¹⁹, ck=ab²k, dk=ab⁴k, ek=ab¹⁹, fk=ab²¹, gk=b²², hk=ab²³, ik=b²⁴, jk=ab²⁵, k²=b²⁶, b⁷l=ab²¹, cl=ab²l, dl=ab⁴l, el=ab⁶l, fl=b²², gl=ab²³, hl=b²⁴, il=ab²⁵, jl=b²⁶, kl=ab²⁷, l²=b²⁸, b⁸m=b²³, cm=ab²m, dm=ab⁴m, em=ab⁶m, fm=ab²³, gm=b²⁴, hm=ab²⁵, im=b²⁶, jm=ab²⁷, km=b²⁸, lm=ab²⁹, m²=b³⁰, b⁹n=ab²⁵, cn=ab²n, dn=ab⁴n, en=ab⁶n, fn=ab⁸n, gn=ab²⁵, hn=b²⁶, in=ab²⁷, jn=b²⁸, kn=ab²⁹, ln=b³⁰, mn=ab³¹, n²=b³², b¹⁰o=b²⁷, co=ab²o, do=ab⁴o, eo=ab⁶o, fo=ab⁸o, go=b⁹o, ho=ab²⁷, io=b²⁸, jo=ab²⁹, ko=b³⁰, lo=ab³¹, mo=b³², no=ab³³, o²=b³², b¹¹p=ab²⁹, cp=ab²p, dp=ab⁴p, ep=ab⁶p, fp=ab⁸p, gp=b⁹p, hp=ab¹⁰p, ip=ab²⁹, jp=b³⁰, kp=ab³¹, lp=b³², mp=ab³³, np=b³², op=ab³³, p²=b³², b¹²q=b³¹, cq=ab²q, dq=ab⁴q, eq=ab⁶q, fq=ab⁸q, gq=b⁹q, hq=ab¹⁰q, iq=b¹¹q, jq=ab³¹, kq=b³², lq=ab³³, mq=b³², nq=ab³³, oq=b³², pq=ab³³, q²=b³², b¹³r=ab³³, cr=ab²r, dr=ab⁴r, er=ab⁶r, fr=ab⁸r, gr=b⁹r, hr=ab¹⁰r, ir=b¹¹r, jr=ab¹²r, kr=ab³³, lr=b³², mr=ab³³, nr=b³², or=ab³³, pr=b³², qr=ab³³, r²=b³², b¹³s=ab¹²r, cs=ab²s, ds=ab⁴s, es=ab⁶s, fs=ab⁸s, gs=b⁹s, hs=ab¹⁰s, is=b¹¹s, js=ab¹²s, ks=ab¹²r, ls=ab³³, ms=b³², ns=ab³³, os=b³², ps=ab³³, qs=b³², rs=ab³³, s²=b³², b¹²t=ab¹¹s, ct=ab²t, dt=ab⁴t, et=ab⁶t, ft=ab⁸t, gt=b⁹t, ht=ab¹⁰t, it=b¹¹t, jt=b¹¹s, kt=ab¹²s, lt=ab¹²r, mt=ab³³, nt=b³², ot=ab³³, pt=b³², qt=ab³³, rt=b³², st=ab³³, t²=b³², b¹¹u=ab¹⁰t, cu=ab²u, du=ab⁴u, eu=ab⁶u, fu=ab⁸u, gu=b⁹u, hu=ab¹⁰u, iu=ab¹⁰t, ju=b¹¹t, ku=b¹¹s, lu=ab¹²s, mu=ab¹²r, nu=ab³³, ou=b³², pu=ab³³, qu=b³², ru=ab³³, su=b³², tu=ab³³, u²=b³², b¹⁰v=ab⁹u, cv=ab²v, dv=ab⁴v, ev=ab⁶v, fv=ab⁸v, gv=b⁹v, hv=b⁹u, iv=ab¹⁰u, jv=ab¹⁰t, kv=b¹¹t, lv=b¹¹s, mv=ab¹²s, nv=ab¹²r, ov=ab³³, pv=b³², qv=ab³³, rv=b³², sv=ab³³, tv=b³², uv=ab³³, v²=b³², b⁹w=ab⁸v, cw=ab²w, dw=ab⁴w, ew=ab⁶w, fw=ab⁸w, gw=ab⁸v, hw=b⁹v, iw=b⁹u, jw=ab¹⁰u, kw=ab¹⁰t, lw=b¹¹t, mw=b¹¹s, nw=ab¹²s, ow=ab¹²r, pw=ab³³, qw=b³², rw=ab³³, sw=b³², tw=ab³³, uw=b³², vw=ab³³, w²=b³², b⁸x=ab⁷w, cx=ab²x, dx=ab⁴x, ex=ab⁶x, fx=b⁷w, gx=ab⁸w, hx=ab⁸v, ix=b⁹v, jx=b⁹u, kx=ab¹⁰u, lx=ab¹⁰t, mx=b¹¹t, nx=b¹¹s, ox=ab¹²s, px=ab¹²r, qx=ab³³, rx=b³², sx=ab³³, tx=b³², ux=ab³³, vx=b³², wx=ab³³, x²=b³², b⁷y=ab⁶x, cy=ab²y, dy=ab⁴y, ey=ab⁶y, fy=b⁷x, gy=b⁷w, hy=ab⁸w, iy=ab⁸v, jy=b⁹v, ky=b⁹u, ly=ab¹⁰u, my=ab¹⁰t, ny=b¹¹t, oy=b¹¹s, py=ab¹²s, qy=ab¹²r, ry=ab³³, sy=b³², ty=ab³³, uy=b³², vy=ab³³, wy=b³², xy=ab³³, y²=b³², b⁶z=ab⁵y, cz=ab²z, dz=ab⁴z, ez=b⁵y, fz=ab⁶x, gz=b⁷x, hz=b⁷w, iz=ab⁸w, jz=ab⁸v, kz=b⁹v, lz=b⁹u, mz=ab¹⁰u, nz=ab¹⁰t, oz=b¹¹t, pz=b¹¹s, qz=ab¹²s, rz=ab¹²r, sz=ab³³, tz=b³², uz=ab³³, vz=b³², wz=ab³³, xz=b³², yz=ab³³, z²=b³², b⁵A=ab⁴z, cA=ab²A, dA=ab⁴A, eA=b⁵z, fA=ab⁶y, gA=ab⁶x, hA=b⁷x, iA=b⁷w, jA=ab⁸w, kA=ab⁸v, lA=b⁹v, mA=b⁹u, nA=ab¹⁰u, oA=ab¹⁰t, pA=b¹¹t, qA=b¹¹s, rA=ab¹²s, sA=ab¹²r, tA=ab³³, uA=b³², vA=ab³³, wA=b³², xA=ab³³, yA=b³², zA=ab³³, A²=b³², b⁴B=ab³A, cB=ab²B, dB=b³A, eB=ab⁴z, fB=b⁵y, gB=ab⁶y, hB=ab⁶x, iB=b⁷x, jB=b⁷w, kB=ab⁸w, lB=ab⁸v, mB=b⁹v, nB=b⁹u, oB=ab¹⁰u, pB=ab¹⁰t, qB=b¹¹t, rB=b¹¹s, sB=ab¹²s, tB=ab¹²r, uB=ab³³, vB=b³², wB=ab³³, xB=b³², yB=ab³³, zB=b³², AB=ab³³, B²=b³², b³C=ab²B, cC=ab²C, dC=b³B, eC=ab⁴A, fC=b⁵z, gC=b⁵y, hC=ab⁶y, iC=ab⁶x, jC=b⁷x, kC=b⁷w, lC=ab⁸w, mC=ab⁸v, nC=b⁹v, oC=b⁹u, pC=ab¹⁰u, qC=ab¹⁰t, rC=b¹¹t, sC=b¹¹s, tC=ab¹²s, uC=ab¹²r, vC=ab³³, wC=b³², xC=ab³³, yC=b³², zC=ab³³, AC=b³², BC=ab³³, C²=b³², b²D=abC, cD=bC, dD=ab²B, eD=b³A, fD=ab⁴z, gD=b⁵z, hD=b⁵y, iD=ab⁶y, jD=ab⁶x, kD=b⁷x, lD=b⁷w, mD=ab⁸w, nD=ab⁸v, oD=b⁹v, pD=b⁹u, qD=ab¹⁰u, rD=ab¹⁰t, sD=b¹¹t, tD=b¹¹s, uD=ab¹²s, vD=ab¹²r, wD=ab³³, xD=b³², yD=ab³³, zD=b³², AD=ab³³, BD=b³², CD=ab³³, D²=b³², bE=aD, cE=bD, dE=ab²C, eE=b³B, fE=ab⁴A, gE=ab⁴z, hE=b⁵z, iE=b⁵y, jE=ab⁶y, kE=ab⁶x, lE=b⁷x, mE=b⁷w, nE=ab⁸w, oE=ab⁸v, pE=b⁹v, qE=b⁹u, rE=ab¹⁰u, sE=ab¹⁰t, tE=b¹¹t, uE=b¹¹s, vE=ab¹²s, wE=ab¹²r, xE=ab³³, yE=b³², zE=ab³³, AE=b³², BE=ab³³, CE=b³², DE=ab³³, E²=b³², bF=aE, cF=aD, dF=bC, eF=ab²B, fF=b³A, gF=ab⁴A, hF=ab⁴z, iF=b⁵z, jF=b⁵y, kF=ab⁶y, lF=ab⁶x, mF=b⁷x, nF=b⁷w, oF=ab⁸w, pF=ab⁸v, qF=b⁹v, rF=b⁹u, sF=ab¹⁰u, tF=ab¹⁰t, uF=b¹¹t, vF=b¹¹s, wF=ab¹²s, xF=ab¹²r, yF=ab³³, zF=b³², AF=ab³³, BF=b³², CF=ab³³, DF=b³², EF=ab³³, F²=b³², b⁵G=aF, cG=ab²G, dG=ab⁴G, eG=aE, fG=bD, gG=bC, hG=ab²C, iG=ab²B, jG=b³B, kG=b³A, lG=ab⁴A, mG=ab⁴z, nG=b⁵z, oG=b⁵y, pG=ab⁶y, qG=ab⁶x, rG=b⁷x, sG=b⁷w, tG=ab⁸w, uG=ab⁸v, vG=b⁹v, wG=b⁹u, xG=ab¹⁰u, yG=ab¹⁰t, zG=b¹¹t, AG=b¹¹s, BG=ab¹²s, CG=ab¹²r, DG=ab³³, EG=b³², FG=ab³³, G²=b³²>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, b²⁸, b³⁰, b³², ag, bh, ai, ab²i, bj, b³j, ak, ab²k, ab⁴k, bl, b³l, b⁵l, am, ab²m, ab⁴m, ab⁶m, bn, b³n, b⁵n, b⁷n, ao, ab²o, ab⁴o, ab⁶o, ab⁸o, bp, b³p, b⁵p, b⁷p, b⁹p, aq, ab²q, ab⁴q, ab⁶q, ab⁸q, ab¹⁰q, br, b³r, b⁵r, b⁷r, b⁹r, b¹¹r, 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, bD, aE, aG, ab²G, ab⁴G}

Phi = 1 a b a b a b c b³ d b⁵ e b⁷ 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 E F b⁴G ab³G b²G abG G

Monoid Structure