Details Page for 0.5411

Complete Solution is Known:

MSV File: q-0.5411.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₉₈(0.5411):

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, b³=b, b²c³=c³, c⁴=b²c², bd=ab, cd=ac, d³=ad², b²ce=ce, c²e=c³, d²e=ade, be²=bc², ce²=c³, de²=ae², e³=c³, bf=ab, c³f=ac³, df=af, ef=de, c²f²=e², f³=af², cg=ce, dg=ag, eg=ce, f²g=afg, bg²=bc², fg²=ag², g³=c³, bh=ab, c³h=ac³, dh=ah, ceh=ace, e²h=c²h, fh=ah, gh=fg, c²h²=g², h³=ah², ci=ce, di=ai, ei=ce, fi=ai, gi=ce, h²i=ahi, bi²=bc², hi²=ai², i³=c³, bj=ab, c³j=ac³, dj=aj, cej=ace, e²j=c²j, fj=aj, g²j=c²j, hj=aj, ij=hi, c²j²=i², j³=aj², ck=ce, dk=ak, ek=ce, fk=ak, gk=ce, hk=ak, ik=ce, j²k=ajk, bk²=bc², jk²=ak², k³=c³, bl=ab, c³l=ac³, dl=al, cel=ace, e²l=c²l, fl=al, g²l=c²l, hl=al, i²l=c²l, jl=al, kl=jk, c²l²=k², l³=al², cm=ce, dm=am, em=ce, fm=am, gm=ce, hm=am, im=ce, jm=am, km=ce, l²m=alm, bm²=bc², lm²=am², m³=c³, bn=ab, c³n=ac³, dn=an, cen=ace, e²n=c²n, fn=an, g²n=c²n, hn=an, i²n=c²n, jn=an, k²n=c²n, ln=an, mn=lm, c²n²=m², n³=an², co=ce, do=ao, eo=ce, fo=ao, go=ce, ho=ao, io=ce, jo=ao, ko=ce, lo=ao, mo=ce, n²o=ano, bo²=bc², no²=ao², o³=c³, bp=ab, c³p=ac³, dp=ap, cep=ace, e²p=c²p, fp=ap, g²p=c²p, hp=ap, i²p=c²p, jp=ap, k²p=c²p, lp=ap, m²p=c²p, np=ap, op=no, c²p²=o², p³=ap², cq=ce, dq=aq, eq=ce, fq=aq, gq=ce, hq=aq, iq=ce, jq=aq, kq=ce, lq=aq, mq=ce, nq=aq, oq=ce, p²q=apq, bq²=bc², pq²=aq², q³=c³, br=ab, c³r=ac³, dr=ar, cer=ace, e²r=c²r, fr=ar, g²r=c²r, hr=ar, i²r=c²r, jr=ar, k²r=c²r, lr=ar, m²r=c²r, nr=ar, o²r=c²r, pr=ar, qr=pq, c²r²=q², r³=ar², cs=ce, ds=as, es=ce, fs=as, gs=ce, hs=as, is=ce, js=as, ks=ce, ls=as, ms=ce, ns=as, os=ce, ps=as, qs=ce, r²s=ars, bs²=bc², rs²=as², s³=c³, bt=ab, c³t=ac³, dt=at, cet=ace, e²t=c²t, ft=at, g²t=c²t, ht=at, i²t=c²t, jt=at, k²t=c²t, lt=at, m²t=c²t, nt=at, o²t=c²t, pt=at, q²t=c²t, rt=at, st=rs, c²t²=s², t³=at², cu=ce, du=au, eu=ce, fu=au, gu=ce, hu=au, iu=ce, ju=au, ku=ce, lu=au, mu=ce, nu=au, ou=ce, pu=au, qu=ce, ru=au, su=ce, t²u=atu, bu²=bc², tu²=au², u³=c³, bv=ab, c³v=ac³, dv=av, cev=ace, e²v=c²v, fv=av, g²v=c²v, hv=av, i²v=c²v, jv=av, k²v=c²v, lv=av, m²v=c²v, nv=av, o²v=c²v, pv=av, q²v=c²v, rv=av, s²v=c²v, tv=av, uv=tu, c²v²=u², v³=av², cw=ce, dw=aw, ew=ce, fw=aw, gw=ce, hw=aw, iw=ce, jw=aw, kw=ce, lw=aw, mw=ce, nw=aw, ow=ce, pw=aw, qw=ce, rw=aw, sw=ce, tw=aw, uw=ce, v²w=avw, bw²=bc², vw²=aw², w³=c³, bx=ab, c³x=ac³, dx=ax, cex=ace, e²x=c²x, fx=ax, g²x=c²x, hx=ax, i²x=c²x, jx=ax, k²x=c²x, lx=ax, m²x=c²x, nx=ax, o²x=c²x, px=ax, q²x=c²x, rx=ax, s²x=c²x, tx=ax, u²x=c²x, vx=ax, wx=vw, c²x²=w², x³=ax², cy=ce, dy=ay, ey=ce, fy=ay, gy=ce, hy=ay, iy=ce, jy=ay, ky=ce, ly=ay, my=ce, ny=ay, oy=ce, py=ay, qy=ce, ry=ay, sy=ce, ty=ay, uy=ce, vy=ay, wy=ce, x²y=axy, by²=bc², xy²=ay², y³=c³, bz=ab, c³z=ac³, dz=az, cez=ace, e²z=c²z, fz=az, g²z=c²z, hz=az, i²z=c²z, jz=az, k²z=c²z, lz=az, m²z=c²z, nz=az, o²z=c²z, pz=az, q²z=c²z, rz=az, s²z=c²z, tz=az, u²z=c²z, vz=az, w²z=c²z, xz=az, yz=xy, c²z²=y², z³=az², cA=ce, dA=aA, eA=ce, fA=aA, gA=ce, hA=aA, iA=ce, jA=aA, kA=ce, lA=aA, mA=ce, nA=aA, oA=ce, pA=aA, qA=ce, rA=aA, sA=ce, tA=aA, uA=ce, vA=aA, wA=ce, xA=aA, yA=ce, zA=ab²A, A²=b²c², bB=ab, c³B=ac³, dB=aB, ceB=ace, e²B=c²B, fB=aB, g²B=c²B, hB=aB, i²B=c²B, jB=aB, k²B=c²B, lB=aB, m²B=c²B, nB=aB, o²B=c²B, pB=aB, q²B=c²B, rB=aB, s²B=c²B, tB=aB, u²B=c²B, vB=aB, w²B=c²B, xB=aB, y²B=c²B, zB=aB, AB=ab²A, B²=b², cC=ce, dC=aC, eC=ce, fC=aC, gC=ce, hC=aC, iC=ce, jC=aC, kC=ce, lC=aC, mC=ce, nC=aC, oC=ce, pC=aC, qC=ce, rC=aC, sC=ce, tC=aC, uC=ce, vC=aC, wC=ce, xC=aC, yC=ce, zC=aC, AC=ce, BC=ab²C, C²=b²c²>

P = {a, b², c², b²c², d², ae, abce, e², cf, f², ag, g², ch, eh, h², ai, i², cj, ej, gj, j², ak, k², cl, el, gl, il, l², am, m², cn, en, gn, in, kn, n², ao, o², cp, ep, gp, ip, kp, mp, p², aq, q², cr, er, gr, ir, kr, mr, or, r², as, s², ct, et, gt, it, kt, mt, ot, qt, t², au, u², cv, ev, gv, iv, kv, mv, ov, qv, sv, v², aw, w², cx, ex, gx, ix, kx, mx, ox, qx, sx, ux, x², ay, y², cz, ez, gz, iz, kz, mz, oz, qz, sz, uz, wz, z², aA, cB, eB, gB, iB, kB, mB, oB, qB, sB, uB, wB, yB, aC}

Phi = 1 a 1 a b b b c a ab² d b b b e ab² ab² f b b b g ab² ab² h b b b i ab² ab² j b b b k ab² ab² l b b b m ab² ab² n b b b o ab² ab² p b b b q ab² ab² r b b b s ab² ab² t b b b u ab² ab² v b b b w ab² ab² x b b b y ab² ab² z b b b A ab² ab² B b b b C ab² ab²

Monoid Structure