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 Q₄₃(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, b³³=b³¹, 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=ab³¹, 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=ab³¹, np=b³², op=ab³¹, p²=b³², b¹²q=b³¹, cq=ab²q, dq=ab⁴q, eq=ab⁶q, fq=ab⁸q, gq=b⁹q, hq=ab¹⁰q, iq=b¹¹q, jq=ab³¹, kq=b³², lq=ab³¹, mq=b³², nq=ab³¹, oq=b³², pq=ab³¹, q²=b³², b¹³r=ab³¹, cr=ab²r, dr=ab⁴r, er=ab⁶r, fr=ab⁸r, gr=b⁹r, hr=ab¹⁰r, ir=b¹¹r, jr=ab¹²r, kr=ab³¹, lr=b³², mr=ab³¹, nr=b³², or=ab³¹, pr=b³², qr=ab³¹, r²=b³², b¹²s=ab¹¹r, cs=ab²s, ds=ab⁴s, es=ab⁶s, fs=ab⁸s, gs=b⁹s, hs=ab¹⁰s, is=b¹¹s, js=b¹¹r, ks=ab¹²r, ls=ab³¹, ms=b³², ns=ab³¹, os=b³², ps=ab³¹, qs=b³², rs=ab³¹, s²=b³², b¹¹t=ab¹⁰s, ct=ab²t, dt=ab⁴t, et=ab⁶t, ft=ab⁸t, gt=b⁹t, ht=ab¹⁰t, it=ab¹⁰s, jt=b¹¹s, kt=b¹¹r, lt=ab¹²r, mt=ab³¹, nt=b³², ot=ab³¹, pt=b³², qt=ab³¹, rt=b³², st=ab³¹, t²=b³², b¹⁰u=ab⁹t, cu=ab²u, du=ab⁴u, eu=ab⁶u, fu=ab⁸u, gu=b⁹u, hu=b⁹t, iu=ab¹⁰t, ju=ab¹⁰s, ku=b¹¹s, lu=b¹¹r, mu=ab¹²r, nu=ab³¹, ou=b³², pu=ab³¹, qu=b³², ru=ab³¹, su=b³², tu=ab³¹, u²=b³², b⁹v=ab⁸u, cv=ab²v, dv=ab⁴v, ev=ab⁶v, fv=ab⁸v, gv=ab⁸u, hv=b⁹u, iv=b⁹t, jv=ab¹⁰t, kv=ab¹⁰s, lv=b¹¹s, mv=b¹¹r, nv=ab¹²r, ov=ab³¹, pv=b³², qv=ab³¹, rv=b³², sv=ab³¹, tv=b³², uv=ab³¹, v²=b³², b⁸w=ab⁷v, cw=ab²w, dw=ab⁴w, ew=ab⁶w, fw=b⁷v, gw=ab⁸v, hw=ab⁸u, iw=b⁹u, jw=b⁹t, kw=ab¹⁰t, lw=ab¹⁰s, mw=b¹¹s, nw=b¹¹r, ow=ab¹²r, pw=ab³¹, qw=b³², rw=ab³¹, sw=b³², tw=ab³¹, uw=b³², vw=ab³¹, w²=b³², b⁷x=ab⁶w, cx=ab²x, dx=ab⁴x, ex=ab⁶x, fx=b⁷w, gx=b⁷v, hx=ab⁸v, ix=ab⁸u, jx=b⁹u, kx=b⁹t, lx=ab¹⁰t, mx=ab¹⁰s, nx=b¹¹s, ox=b¹¹r, px=ab¹²r, qx=ab³¹, rx=b³², sx=ab³¹, tx=b³², ux=ab³¹, vx=b³², wx=ab³¹, x²=b³², b⁶y=ab⁵x, cy=ab²y, dy=ab⁴y, ey=b⁵x, fy=ab⁶w, gy=b⁷w, hy=b⁷v, iy=ab⁸v, jy=ab⁸u, ky=b⁹u, ly=b⁹t, my=ab¹⁰t, ny=ab¹⁰s, oy=b¹¹s, py=b¹¹r, qy=ab¹²r, ry=ab³¹, sy=b³², ty=ab³¹, uy=b³², vy=ab³¹, wy=b³², xy=ab³¹, y²=b³², b⁵z=ab⁴y, cz=ab²z, dz=ab⁴z, ez=b⁵y, fz=ab⁶x, gz=ab⁶w, hz=b⁷w, iz=b⁷v, jz=ab⁸v, kz=ab⁸u, lz=b⁹u, mz=b⁹t, nz=ab¹⁰t, oz=ab¹⁰s, pz=b¹¹s, qz=b¹¹r, rz=ab¹²r, sz=ab³¹, tz=b³², uz=ab³¹, vz=b³², wz=ab³¹, xz=b³², yz=ab³¹, z²=b³², b⁴A=ab³z, cA=ab²A, dA=b³z, eA=ab⁴y, fA=b⁵x, gA=ab⁶x, hA=ab⁶w, iA=b⁷w, jA=b⁷v, kA=ab⁸v, lA=ab⁸u, mA=b⁹u, nA=b⁹t, oA=ab¹⁰t, pA=ab¹⁰s, qA=b¹¹s, rA=b¹¹r, sA=ab¹²r, tA=ab³¹, uA=b³², vA=ab³¹, wA=b³², xA=ab³¹, yA=b³², zA=ab³¹, A²=b³², b³B=ab²A, cB=ab²B, dB=b³A, eB=ab⁴z, fB=b⁵y, gB=b⁵x, hB=ab⁶x, iB=ab⁶w, jB=b⁷w, kB=b⁷v, lB=ab⁸v, mB=ab⁸u, nB=b⁹u, oB=b⁹t, pB=ab¹⁰t, qB=ab¹⁰s, rB=b¹¹s, sB=b¹¹r, tB=ab¹²r, uB=ab³¹, vB=b³², wB=ab³¹, xB=b³², yB=ab³¹, zB=b³², AB=ab³¹, B²=b³², b²C=abB, cC=bB, dC=ab²A, eC=b³z, fC=ab⁴y, gC=b⁵y, hC=b⁵x, iC=ab⁶x, jC=ab⁶w, kC=b⁷w, lC=b⁷v, mC=ab⁸v, nC=ab⁸u, oC=b⁹u, pC=b⁹t, qC=ab¹⁰t, rC=ab¹⁰s, sC=b¹¹s, tC=b¹¹r, uC=ab¹²r, vC=ab³¹, wC=b³², xC=ab³¹, yC=b³², zC=ab³¹, AC=b³², BC=ab³¹, C²=b³², bD=aC, cD=bC, dD=ab²B, eD=b³A, fD=ab⁴z, gD=ab⁴y, hD=b⁵y, iD=b⁵x, jD=ab⁶x, kD=ab⁶w, lD=b⁷w, mD=b⁷v, nD=ab⁸v, oD=ab⁸u, pD=b⁹u, qD=b⁹t, rD=ab¹⁰t, sD=ab¹⁰s, tD=b¹¹s, uD=b¹¹r, vD=ab¹²r, wD=ab³¹, xD=b³², yD=ab³¹, zD=b³², AD=ab³¹, BD=b³², CD=ab³¹, D²=b³², bE=aD, cE=aC, dE=bB, eE=ab²A, fE=b³z, gE=ab⁴z, hE=ab⁴y, iE=b⁵y, jE=b⁵x, kE=ab⁶x, lE=ab⁶w, mE=b⁷w, nE=b⁷v, oE=ab⁸v, pE=ab⁸u, qE=b⁹u, rE=b⁹t, sE=ab¹⁰t, tE=ab¹⁰s, uE=b¹¹s, vE=b¹¹r, wE=ab¹²r, xE=ab³¹, yE=b³², zE=ab³¹, AE=b³², BE=ab³¹, CE=b³², DE=ab³¹, E²=b³², bF=aE, cF=aD, dF=bC, eF=ab²B, fF=b³A, gF=b³z, hF=ab⁴z, iF=ab⁴y, jF=b⁵y, kF=b⁵x, lF=ab⁶x, mF=ab⁶w, nF=b⁷w, oF=b⁷v, pF=ab⁸v, qF=ab⁸u, rF=b⁹u, sF=b⁹t, tF=ab¹⁰t, uF=ab¹⁰s, vF=b¹¹s, wF=b¹¹r, xF=ab¹²r, yF=ab³¹, zF=b³², AF=ab³¹, BF=b³², CF=ab³¹, DF=b³², EF=ab³¹, F²=b³², b⁴G=F, cG=ab²G, dG=aF, eG=aD, fG=bC, gG=bB, hG=ab²B, iG=ab²A, jG=b³A, kG=b³z, lG=ab⁴z, mG=ab⁴y, nG=b⁵y, oG=b⁵x, pG=ab⁶x, qG=ab⁶w, rG=b⁷w, sG=b⁷v, tG=ab⁸v, uG=ab⁸u, vG=b⁹u, wG=b⁹t, xG=ab¹⁰t, yG=ab¹⁰s, zG=b¹¹s, AG=b¹¹r, BG=ab¹²r, CG=ab³¹, DG=b³², EG=ab³¹, FG=b³², 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, 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, aE, bG, b³G}

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 ab³G b²G abG G

Monoid Structure