Details Page for 0.3135

Complete Solution is Known:

MSV File: q-0.3135.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₂₂(0.3135):

Q = <a,b,c,d,e,f,g,h,i,j,k | a²=1, b³=b, b²c=c, c⁵=c⁴, b²d=d, c⁴d=ac⁴, d²=c⁴, b²e=e, c⁴e=bc⁴, c³e²=c³, c²e³=c²e, e⁴=e², b²f=f, c⁴f=ac⁴, ce³f=cef, c²f²=c², cef²=ce³, e²f²=e², cf³=cf, f⁴=f², b²g=g, cg=bc², e²g²=c²e², f²g²=c², g⁵=bg⁴, b²h=h, c⁴h=ac⁴, ef³h=efh, de³fgh=defgh, def²gh=de³gh, efg²h=c²efh, fg³h=bc³fh, g⁴h=fg⁴, c³h²=c³, eh²=e³, cf²h²=ch², g³h²=bc³, c²h³=c²h, cdh³=cdf²h, fg²h³=fg²h, h⁴=h², b²i=i, c²i=c³, e²i=ce², cefi=c²ef, efgi=befg², g²i=bg³, f³hi=fhi, f²h²i=h²i, ch³i=cf²hi, cei²=c³e, cf²i²=ci², egi²=eg³, chi²=c³h, gh²i²=bc³, ci³=c⁴, ei³=beg³, gi³=bg⁴, h³i³=f²hi³, i⁴=g⁴, b²j=j, c³j=bc³e, cej=bce², e²j=be³, g⁴j=g⁴, c²hj=bc²eh, cdhj=bcdeh, defhj=bde²fh, f³hj=fhj, fg²hj=bc²efh, ch²j=bce³, f²h²j=h²j, gh²j=be³g, cij=bcei, egij=beg²j, f²gij=ef²i², fghij=efhi², h²ij=bce³, i²j=bgij, cf²j²=cj², efgj²=efg, eg²j²=eg², g³j²=g³, dfghj²=de²fgh, dh³j²=df²hj², f²ij²=bef²ij, fhij²=befhij, ghij²=bg²hj², cj³=cf²j, egj³=egj, g²j³=g²j, dehj³=dehj, dfhj³=dfh³j, h²j³=h²j, ej⁴=ej², gj⁴=gj², dhj⁴=dhj², j⁵=j³, b²k=k, c³k=bc⁴, ef²k=e³k, g²k=c²k, e³fhk=efhk, ch²k=cf²k, dfh³k=dfhk, cfik=c²fk, gik=bcik, efhik=cefhk, h²ik=f²ik, ci²k=bc⁴, ei²k=ceik, f³i²k=fi²k, i³k=bc⁴, cjk=bcek, dhjk=bdehk, ehjk=be²hk, h²jk=be³k, f²ijk=bce³k, hijk=behik, defj²k=defk, f²hj²k=hj²k, ej³k=ejk, fgj³k=fgjk, hj³k=f²hjk, dfij³k=dfijk, ij⁴k=ij²k, c²ek²=bc²ek, ce³k²=cek², de³fk²=defk², cf²k²=ck², df³k²=dfk², egk²=bcek², f²gk²=gk², de³hk²=dehk², df²hk²=dhk², f³hk²=fhk², h²k²=f²k², cik²=c²k², defik²=cdefk², dehik²=cdehk², f²i²k²=i²k², jk²=bek², ck³=bck², ek³=be³k², f²k³=k³, gk³=ck², ik³=bf²ik², k⁴=bk³>

P = {a, b², c, c², c³, c⁴, bd, acd, ac²d, ac³d, be, bce, bc²e, bc³e, ade, abc²de, abc³de, e², ce², c²e², bde², acde², ac²de², be³, bce³, ade³, f, acf, ac²f, ac³f, bdf, c²df, c³df, bef, bcef, abc²ef, abc³ef, def, cdef, bc³def, e²f, ace²f, ac²e²f, bde²f, c²de²f, be³f, de³f, f², cf², bdf², acdf², bef², adef², f³, bdf³, bef³, def³, bg, dg, eg, be²g, e³g, bfg, efg, bdefg, be²fg, e³fg, bde³fg, bf²g, ef²g, bf³g, ef³g, bdef³g, g², bdg², beg², fg², befg², bg³, dg³, eg³, bfg³, efg³, g⁴, bdg⁴, beg⁴, fg⁴, befg⁴, h, ach, ac²h, ac³h, bdh, bcdh, c³dh, beh, bceh, abc²eh, abc³eh, deh, bc²deh, bc³deh, e²h, ace²h, ac²e²h, bde²h, bcde²h, be³h, bce³h, de³h, fh, cfh, c²fh, c³fh, bdfh, abcdfh, abc²dfh, befh, bcefh, bc²efh, bc³efh, defh, acdefh, abc³defh, e²fh, ce²fh, c²e²fh, bde²fh, abcde²fh, abc²de²fh, be³fh, de³fh, f²h, acf²h, bdf²h, bcdf²h, bef²h, def²h, f³h, bdf³h, bgh, dgh, egh, be²gh, de²gh, e³gh, bfgh, adfgh, efgh, abdefgh, be²fgh, ade²fgh, e³fgh, bf²gh, df²gh, ef²gh, bf³gh, adf³gh, g²h, beg²h, fg²h, abdfg²h, bg³h, eg³h, h², ch², c²h², bdh², acdh², ac²dh², fh², acfh², ac²fh², bdfh², c²dfh², f²h², bdf²h², f³h², bdf³h², bgh², dgh², bfgh², bf²gh², bf³gh², g²h², fg²h², h³, ach³, bdh³, fh³, cfh³, bdfh³, f²h³, bdf²h³, f³h³, bdf³h³, bgh³, dgh³, bfgh³, adfgh³, bf²gh³, df²gh³, bf³gh³, adf³gh³, g²h³, i, ci, bdi, acdi, bei, bcei, abcdei, fi, acfi, bdfi, befi, defi, f²i, cf²i, bdf²i, acdf²i, bef²i, f³i, bdf³i, bef³i, def³i, bgi, dgi, egi, bfgi, bf²gi, bf³gi, hi, achi, bdhi, behi, abcehi, bcdehi, fhi, cfhi, bdfhi, abcdfhi, befhi, adefhi, f²hi, acf²hi, bdf²hi, bef²hi, bghi, eghi, bfghi, adfghi, bf²ghi, h²i, ch²i, bdh²i, acdh²i, fh²i, acfh²i, bdfh²i, bgh²i, bfgh²i, h³i, bdh³i, fh³i, bdfh³i, bgh³i, bfgh³i, adfgh³i, i², ci², bdi², acdi², bei², fi², acfi², bdfi², befi², f²i², bdf²i², bef²i², f³i², bdf³i², bef³i², bgi², dgi², bfgi², bf²gi², bf³gi², hi², behi², fhi², adfhi², befhi², af²hi², bef²hi², bghi², bfghi², bf²ghi², h²i², adh²i², afh²i², ah³i², fh³i², adfh³i², i³, bdi³, fi³, f²i³, adf²i³, af³i³, hi³, fhi³, adfhi³, af²hi³, df²hi³, h²i³, adh²i³, afh²i³, dfh²i³, j, cj, c²j, bdj, acdj, ac²dj, bej, fj, acfj, ac²fj, bdfj, c²dfj, befj, defj, f²j, cf²j, bdf²j, acdf²j, bef²j, f³j, bdf³j, bef³j, def³j, bgj, dgj, egj, bfgj, efgj, bf²gj, ef²gj, adef²gj, bf³gj, aef³gj, g²j, bdg²j, beg²j, fg²j, befg²j, bg³j, dg³j, eg³j, bfg³j, efg³j, hj, achj, bdhj, behj, dehj, fhj, cfhj, bdfhj, befhj, f²hj, acf²hj, bdf²hj, bef²hj, bghj, eghj, bdeghj, bfghj, adfghj, efghj, bf²ghj, aef²ghj, g²hj, beg²hj, bg³hj, eg³hj, h²j, bdh²j, fh²j, bdfh²j, h³j, bdh³j, fh³j, bdfh³j, ij, bdij, beij, fij, bdfij, befij, f²ij, bdf²ij, bef²ij, f³ij, bdf³ij, bef³ij, bgij, dgij, bfgij, hij, behij, dehij, fhij, abdfhij, befhij, f²hij, bef²hij, bghij, j², cj², c²j², bdj², acdj², ac²dj², bej², adej², fj², acfj², ac²fj², bdfj², c²dfj², befj², defj², f²j², bdf²j², bef²j², adef²j², f³j², bdf³j², bef³j², def³j², bgj², dgj², egj², bfgj², bf²gj², bf³gj², g²j², bdg²j², fg²j², hj², achj², bdhj², behj², dehj², fhj², cfhj², bdfhj², befhj², f²hj², bdf²hj², bef²hj², bghj², dghj², eghj², bfghj², bf²ghj², g²hj², h²j², bdh²j², fh²j², bdfh²j², h³j², fh³j², ij², bdij², beij², fij², befij², defij², bgij², dgij², bfgij², hij², bdhij², behij², j³, bdj³, bej³, fj³, bdfj³, befj³, defj³, f²j³, bdf²j³, bef²j³, f³j³, bdf³j³, bef³j³, def³j³, bgj³, dgj³, bfgj³, bf²gj³, bf³gj³, hj³, bdhj³, behj³, fhj³, befhj³, f²hj³, bef²hj³, bghj³, bfghj³, bf²ghj³, ij³, bdij³, beij³, fij³, bdfij³, befij³, bgij³, dgij³, bfgij³, hij³, behij³, j⁴, bdj⁴, fj⁴, bdfj⁴, f²j⁴, bdf²j⁴, f³j⁴, bdf³j⁴, hj⁴, fhj⁴, f²hj⁴, ij⁴, bdij⁴, fij⁴, hij⁴, bk, bck, bc²k, adk, abc²dk, ek, cek, c²ek, bdek, acdek, ac²dek, be²k, bce²k, bc²e²k, abc²de²k, e³k, ce³k, bde³k, acde³k, bfk, bcfk, abc²fk, dfk, efk, acefk, ac²efk, bdefk, c²defk, be²fk, bce²fk, abc²e²fk, de²fk, e³fk, bde³fk, bf²k, bcf²k, adf²k, bf³k, df³k, gk, begk, e²gk, be³gk, fgk, bdfgk, befgk, e²fgk, be³fgk, f²gk, f³gk, bhk, bchk, abc²hk, dhk, bc²dhk, ehk, acehk, ac²ehk, bdehk, c²dehk, be²hk, bce²hk, abc²e²hk, de²hk, bc²de²hk, e³hk, ace³hk, bde³hk, bfhk, bcfhk, bc²fhk, dfhk, acdfhk, efhk, cefhk, c²efhk, bdefhk, abcdefhk, be²fhk, bce²fhk, bc²e²fhk, de²fhk, acde²fhk, bf²hk, bcf²hk, df²hk, bf³hk, df³hk, ghk, beghk, e²ghk, be³ghk, fghk, abdfghk, befghk, adefghk, e²fghk, abde²fghk, f²ghk, f³ghk, abdf³ghk, bh²k, adh²k, bfh²k, dfh²k, bf²h²k, adf²h²k, bf³h²k, df³h²k, gh²k, fgh²k, bdfgh²k, f²gh²k, f³gh²k, bh³k, dh³k, bfh³k, bf²h³k, bf³h³k, gh³k, fgh³k, f²gh³k, f³gh³k, bik, bcik, abcdik, eik, ceik, adeik, acdeik, bfik, dfik, aefik, bf²ik, bf³ik, df³ik, bhik, abchik, bcdhik, aehik, acehik, bdehik, bfhik, bf²hik, bi²k, abdi²k, abfi²k, bf²i²k, abdf²i²k, abhi²k, bdhi²k, bfhi²k, abdfhi²k, abf²hi²k, bdf²hi²k, bjk, ejk, abdejk, bfjk, dfjk, efjk, bdefjk, bf²jk, bf³jk, df³jk, gjk, adgjk, begjk, afgjk, befgjk, defgjk, f²gjk, adf²gjk, af³gjk, bhjk, bfhjk, bf²hjk, aghjk, fghjk, af²ghjk, bijk, abdijk, eijk, abfijk, efijk, bdefijk, bj²k, adj²k, ej²k, bdej²k, bfj²k, dfj²k, efj²k, bf²j²k, adf²j²k, bf³j²k, df³j²k, gj²k, begj²k, fgj²k, bdfgj²k, f²gj²k, f³gj²k, bhj²k, bfhj²k, ghj²k, fghj²k, bij²k, eij²k, adeij²k, bfij²k, dfij²k, aefij²k, bj³k, bfj³k, dfj³k, bf²j³k, bf³j³k, df³j³k, gj³k, adgj³k, bij³k, abdij³k, abfij³k, bj⁴k, adj⁴k, bfj⁴k, dfj⁴k, bf²j⁴k, bf³j⁴k, df³j⁴k, k², ck², c²k², bdk², acdk², ac²dk², bek², bcek², abcdek², e²k², ce²k², abde²k², be³k², fk², acfk², ac²fk², bdfk², c²dfk², befk², abcefk², defk², e²fk², ce²fk², bde²fk², bcde²fk², be³fk², f²k², bdf²k², f³k², bgk², bfgk², hk², achk², ac²hk², bdhk², c²dhk², behk², abcehk², dehk², e²hk², ce²hk², bde²hk², be³hk², fhk², cfhk², c²fhk², bdfhk², abcdfhk², befhk², bcefhk², defhk², acdefhk², e²fhk², ce²fhk², bde²fhk², abcde²fhk², f²hk², bghk², bfghk², adfghk², ik², adik², beik², afik², befik², f²ik², adf²ik², af³ik², ahik², behik², fhik², af²hik², i²k², adi²k², afi²k², dfi²k², ahi²k², dhi²k², fhi²k², adfhi²k², bk³, bfk³, dfk³, bhk³, dhk³, bfhk³, dfhk³}

Phi = 1 a b a b c b b² d b² ef²j² b² e f g h b c b i d j k

Monoid Structure