Details Page for 0.744

Complete Solution is Known:

MSV File: q-0.744.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₃₉(0.744):

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,H,I,J,K,L | a²=1, b³=b, b²c=c, c³=ac², b²d=d, cd=c², d²=c², b²e=e, c²e²=c², ce³=ce, de³=de, e⁴=e², b²f=f, c²f=acf, df=cf, cef=aef, e²f=acf, f²=c², b²g=g, c²g=bc², e³g=eg, cfg=bcf, efg=bef, g²=c², b²h=h, ch=acg, dh=adg, eh=aeg, fh=afg, gh=ac², h²=c², b²i=i, c²i=ac²e, di=ci, e³i=ei, fi=aef, e²gi=gi, hi=agi, i²=aei, b²j=j, cj=cf, dj=cf, ej=ef, fj=c², gj=abcf, hj=bcf, ij=aef, j²=c², b²k=k, ck=cf, ek=ef, fk=c², gk=abcf, hk=bcf, ik=aef, k²=c², b²l=l, c²l=bc², dl=cl, ce²l=cl, e³l=el, fl=abcf, gl=c², hl=ac², il=gi, jl=abcf, kl=abcf, l²=c², b²m=m, cm=c²e, e²m=m, fm=aef, gm=abc²e, hm=bc²e, im=c², jm=aef, km=aef, lm=abc²e, m²=c², b²n=n, cn=c², dn=c², e³n=en, fn=cf, e²gn=gn, hn=agn, e²in=in, gin=cgi, jn=cf, kn=dk, e²ln=ln, mn=c²e, n²=c², b²o=o, c²o=acf, eo=ef, cfo=ac², cgo=bcf, dgo=bco, fgo=bjk, ho=ago, io=aef, jo=c², ko=c², lo=abcf, mo=aef, no=cf, o²=c², b²p=p, c²p=cf, ep=aef, fp=afo, gp=ago, hp=go, ip=ef, jp=ac², kp=ac², lp=bcf, mp=ef, np=acf, op=ac², p²=c², b²q=q, cq=c²e, dq=c²e, e³q=eq, fq=aef, e²gq=gq, hq=agq, iq=c², jq=aef, kq=aef, e²lq=lq, mq=dem, nq=c²e, oq=aef, pq=ef, q²=c², b²r=r, c²r=c²e, dr=cr, e²r=r, fr=ef, gr=bc²e, hr=abc²e, ir=ac², jr=ef, kr=ef, lr=bc²e, mr=ac², nr=ac²e, or=ef, pr=aef, qr=cer, r²=c², b²s=s, cs=cf, ds=cf, es=ef, fs=c², hs=bcf, is=aef, js=jk, ks=jk, ls=abcf, ms=aef, ns=cf, os=c², ps=ac², qs=aef, rs=ef, s²=c², b²t=t, c²t=bc²e, dt=ct, ft=bef, e²gt=gt, ht=agt, jt=bef, kt=bef, clt=cgt, e²lt=lt, mt=abdem, e²nt=nt, gnt=cgt, lnt=cgt, ot=bef, pt=abef, qt=abc², rt=abcer, st=bef, t²=c², b²u=u, c²u=abc², ce²u=cu, de²u=du, e³u=eu, fu=bcf, cgu=c², dgu=abelq, e²gu=gu, hu=agu, e²iu=iu, giu=c²e, ju=bcf, ku=bcf, lu=ac², dmu=bcr, e²nu=nu, gnu=acer, inu=ciu, ou=bcf, pu=abcf, e²qu=qu, gqu=ablq, ru=abc²e, su=bcf, tu=abqu, u²=c², b²v=v, cv=c², dv=c², e²v=v, fv=cf, gv=acegi, hv=cegi, iv=ce²i, jv=cf, kv=cf, lv=acegi, mv=c²e, nv=c², ov=cf, pv=acf, qv=c²e, rv=ac²e, sv=cf, tv=aceit, uv=aceiu, v²=c², b²w=w, dw=cw, cfw=afw, ce²gw=cgw, fgw=bfw, hw=agw, jw=fw, clw=cgw, e²lw=lw, e²nw=nw, gnw=cgw, lnw=cgw, cow=afw, fow=c²w, qw=ac²ew, crw=ac²ew, sw=fw, tw=bc²ew, cuw=bc²w, e²uw=uw, muw=brw, nuw=bc²w, vw=aceiw, w²=c², b²x=x, c²x=bc²e, dx=cx, e²x=x, fx=bef, gx=c²e, hx=ac²e, ix=aex, jx=bef, kx=bef, lx=c²e, mx=abc², nx=cx, ox=bef, px=abef, qx=abc², rx=bc², sx=bef, tx=c², ux=egit, vx=cx, wx=bc²ew, x²=c², b²y=y, c²y=bc²e, dy=cy, ey=bjk, fy=bef, gy=c²e, hy=ac²e, ciy=bjk, jy=bef, ky=bef, ly=c²e, my=abc², ny=abc²e, oy=bef, py=abef, qy=abc², ry=bc², sy=bef, ty=c², uy=ac²e, vy=abc²e, wy=bc²ew, xy=c², y²=c², b²z=z, cz=aelq, dz=aelq, e³z=ez, fz=bcf, gz=ac², hz=c², iz=bc²e, jz=bcf, kz=bcf, lz=ac², mz=bc²e, nz=abcer, oz=bcf, pz=abcf, qz=alq, rz=abc²e, sz=bcf, tz=blq, uz=c², vz=bc², e²wz=wz, xz=ac²e, yz=ac²e, z²=c², b²A=A, cA=c²w, dA=c²w, e³A=eA, fA=afw, hA=agA, e²iA=iA, jA=afw, e²lA=lA, nA=c²w, pA=aoA, qA=c²ew, sA=afw, tA=abc²ew, e²uA=uA, iuA=abc²ew, muA=brA, vA=c²w, iwA=bceit, kwA=dk, mwA=dm, owA=do, rwA=cr, guwA=abelq, xA=abc²ew, yA=abc²ew, zA=bc²w, A²=c², b²B=B, c²B=c²w, e²B=B, fB=fw, gB=bc²w, hB=abc²w, ciB=aceB, jB=fw, kB=fw, lB=bc²w, mB=ac²ew, nB=cB, oB=fw, pB=afw, qB=ac²ew, rB=c²ew, sB=fw, tB=bc²ew, duB=cuB, iuB=aeuB, vB=cB, wB=abcex, xB=bc²ew, yB=bc²ew, zB=abc²w, AB=ac², B²=c², b²C=C, cC=bcx, dC=bcx, e²C=C, fC=ef, gC=abcgt, hC=bcgt, jC=ef, kC=ef, lC=abcgt, mC=ac², nC=bcx, oC=ef, pC=aef, qC=cer, rC=c², sC=ef, tC=abcer, uC=begit, vC=bcx, iwC=ac²w, xC=bc², yC=bc², zC=abc²e, AC=rA, BC=c²ew, C²=c², b²D=D, cD=c², dD=c², eD=ac²e, fD=cf, gD=abc², hD=bc², iD=c²e, jD=cf, kD=cf, lD=abc², mD=c²e, nD=c², oD=cf, pD=acf, qD=c²e, rD=ac²e, sD=cf, tD=abc²e, uD=bc², vD=c², wD=ac²w, xD=abc²e, yD=abc²e, zD=bc², AD=c²w, BD=ac²w, CD=ac²e, D²=c², b²E=E, cE=cr, dE=cr, e²E=E, fE=ef, gE=bc²e, hE=abc²e, iE=acgit, jE=ef, kE=ef, lE=bc²e, mE=ac², nE=ac²e, oE=ef, pE=aef, qE=cer, rE=c², sE=ef, tE=abcer, uE=abc²e, vE=ac²e, wE=abewz, xE=bc², yE=bc², zE=abc²e, AE=ac²ew, BE=c²ew, CE=c², DE=ac²e, E²=c², b²F=F, cF=afw, dF=afw, eF=efw, fF=c²w, gF=bfw, hF=abfw, iF=aefw, jF=c²w, lF=bfw, mF=aefw, nF=afw, oF=c²w, pF=ac²w, qF=aefw, rF=efw, sF=c²w, tF=befw, uF=abfw, vF=afw, kwF=jk, xF=befw, yF=befw, zF=abfw, AF=cf, BF=acf, CF=efw, DF=afw, EF=efw, F²=c², b²G=G, cG=bc²w, dG=bc²w, e³G=eG, fG=abfw, gG=ac²w, hG=c²w, iG=bc²ew, jG=abfw, kG=abfw, lG=ac²w, mG=bc²ew, nG=bc²w, oG=goA, pG=agoA, qG=bc²ew, rG=abc²ew, sG=abfw, tG=ac²ew, uG=guA, vG=bc²w, ewG=gq, xG=ac²ew, yG=ac²ew, zG=c²w, AG=bc², BG=abc², CG=abc²ew, DG=bc²w, EG=abc²ew, FG=bcf, G²=c², b²H=H, c²H=fw, dH=cH, ceH=aefw, e³H=eH, fH=c²w, gH=bfw, hH=abfw, iH=aefw, jH=c²w, kH=c²w, lH=bfw, mH=aefw, nH=afw, oH=kF, cpH=kF, qH=aefw, rH=efw, sH=c²w, tH=befw, uH=abfw, vH=afw, ewH=ef, pwH=biy, xH=befw, yH=befw, zH=abfw, AH=cf, BH=acf, CH=efw, DH=afw, EH=efw, FH=c², GH=bcf, H²=c², b²I=I, c²I=acI, dI=cI, e²I=I, cfI=afI, gI=abcI, hI=bcI, ciI=aceI, jI=fI, kI=fI, lI=abcI, mI=ceI, nI=cI, oI=fI, pI=afI, qI=ceI, rI=aceI, sI=fI, ctI=bceI, uI=bcI, vI=cI, cwI=awI, iwI=aewI, xI=abceI, yI=abceI, zI=bcI, AI=awI, BI=wI, CI=aceI, DI=cI, EI=aceI, FI=fwI, GI=abwI, HI=fwI, I²=c², b²J=J, cJ=c²e, dJ=c²e, e²J=J, fJ=aef, gJ=abdm, hJ=bdm, iJ=c², jJ=aef, kJ=aef, lJ=bcr, mJ=c², nJ=c²e, oJ=aef, pJ=ef, qJ=c², rJ=ac², sJ=aef, tJ=abc², vJ=c²e, wJ=ac²ew, xJ=abc², yJ=abc², zJ=bc²e, AJ=c²ew, BJ=ac²ew, CJ=ac², DJ=c²e, EJ=ac², FJ=aefw, GJ=bc²ew, HJ=aefw, IJ=ceI, J²=c², b²K=K, cK=abefw, dK=abefw, eK=bfw, fK=bc²ew, gK=efw, hK=aefw, iK=abfw, jK=bc²ew, lK=efw, mK=abfw, nK=abefw, oK=bc²ew, pK=abc²ew, qK=abfw, rK=bfw, sK=bc²ew, tK=fw, uK=aefw, vK=abefw, wK=bef, xK=fw, yK=fw, zK=aefw, AK=abef, BK=bef, CK=bfw, DK=abefw, EK=bfw, FK=bc²e, GK=aef, HK=bc²e, IK=befwI, JK=abfw, K²=c², b²L=L, cL=c²e, dL=c²e, eL=ac², fL=aef, gL=abc²e, hL=bc²e, iL=c², jL=aef, kL=aef, lL=abc²e, mL=c², nL=c²e, oL=aef, pL=ef, qL=c², rL=ac², sL=aef, tL=abc², uL=bc²e, vL=c²e, wL=ac²ew, xL=abc², yL=abc², zL=bc²e, AL=c²ew, BL=ac²ew, CL=ac², DL=c²e, EL=ac², FL=aefw, GL=bc²ew, HL=aefw, IL=ceI, JL=c², KL=abfw, L²=c²>

P = {a, b², bc, c², ad, ace, e², bce², ade², bf, abg, abdeg, be²g, abce²g, bh, aei, cei, abegi, bcegi, bk, abdk, abl, abcel, be²l, aem, ae²n, ein, aco, fo, cp, abq, aeq, abgq, ablq, er, ags, abt, abcet, be³t, gt, acegt, bit, abe²it, bce²it, git, lt, abent, bu, bceu, bdeu, abe²u, agu, beiu, abceiu, bemu, bqu, aev, aew, abegw, aciw, abcgiw, abelw, mw, ainw, arw, beuw, eguw, abex, aby, biy, bz, abe²z, bewz, awA, ae²wA, abegwA, abelwA, buwA, aceB, bceuB, aeC, iC, bD, eE, aeH, abI, itI, aeJ, beuJ, kK, bL}

Phi = 1 a 1 a ef aef ef b ab c bef abef ef aef ef d e ae bef abef f g h i ai ac² j cf k l al m bef n o p aef q r ar bef abef s t u ac²e c²e v bef acf efw bc² abc² w abcf abef efw acf x ac² c²e ac²e bef abef efw y z A B C befw efw acf D l c²w E abef F kA acf ac² G befw bef abcf efw bc²e abc² c²ew amA abef bcf H iuw bc² bc²e c²w ac²w abef befw ac²e bceit bc² acf abc²w bef abcf c²e bc² I abc²w acf bfw befw ac²e c²e bc² abc² c²ew ac²ew bef acI J c²e bc² acf cf bef abef cer bc² abc² acI K wF befw abfw c²e L aewz c²ew acI c²ew abfw abc²w aefI abc²w aef acI bcI ac² aefI efI abc²w acI aceI acf befw abceI bceI abef abc²w afw acI befw bfw efI aefI bc²w abc²w acI abc² befw ac²ew efI abc²w acI ef aef ac²e bfI ac²ew ac² bc²w aefw abc²e befw afI ac² aefI ac² abc²w acI abefI bfI abc² bcf aefI aefw acI cI befw ac²e c²e ac²e abceI aefw efw acI c²w befw aefI abcI fw cf befI abefI ac²w aefI aefwI aefI afw acf befI befw c²e ac²e bcI efw cf aefwI acI c²w befw bcI fw acf cf ac² ac²w aefwI befw afI fw aefI bfI abc²w befI abceI bcI fw wI awI abc²w c²ew bfw befw abceI ef bfI bc²w c²ew ac²ew acI befw wI bfwI abc²ew abc²w abc²e acf befw afw bcf awI abefwI

Monoid Structure