Details Page for 0.3164

Complete Solution is Known:

MSV File: q-0.3164.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₁(0.3164):

Q = <a,b,c,d,e,f,g,h,i | a²=1, b⁵=b³, b³c=bc, c²=b²c, b³d=b⁴, cd=bc, d⁴=d², b²de=b³e, d³e²=de², bce³=bce, b³e⁴=b³e², bde⁴=bde², e⁵=e³, bcef=abce², bd³ef=bdef, b³f²=b³e², bcf²=bce², b²df²=b³e², d³f²=df², be²f²=bf², ce²f²=cf², de²f²=df², e³f²=ef², f⁴=f², bcg=abc, b²dfg=b³fg, bdf²g=b⁴e²g, b²g²=b²c, cg²=b²c, dg²=bc, beg²=bce, e³g²=eg², bf²g²=bce², ef²g²=eg², g³=ab²c, bceh=abce², b³e²h=abce, ce²h=b²e²h, cf²h=b²f²h, e²f²h=f²h, df³gh=adef²gh, eg²h=ab²ce², f²g²h=ab²ce, bdf²h²=d²ef²gh, f³h²=aef²h², df²gh²=adef²gh, f²h³=aef²h², bde²gh³=bde²gh, bde²h⁴=bde²h², e³h⁴=e³h², bch⁵=b³h⁵, b³eh⁵=abce², ceh⁵=b²eh⁵, bd²eh⁵=bd²e³h³, de²h⁵=de⁴h³, bdefh⁵=bde³fh³, b³gh⁵=ab³h⁵, cfgh⁵=b²fgh⁵, d²eh⁶=d²e³h², be²h⁶=be²h⁴, defh⁶=de³fh², bdeh⁷=bdeh⁵, e²h⁷=e²h⁵, befh⁷=befh⁵, deh⁸=deh⁶, efh⁸=efh⁶, bh¹⁰=bh⁶, ch¹⁰=ch⁶, eh¹⁰=eh⁶, g²h¹⁰=g²h⁶, h¹¹=h⁷, bci=abcf, d³ei=dei, e³i=ei, b²dfi=b³fi, d³fi=dfi, cefi=ab²ef³h, cf²i=ab²f²h, df²i=de²i, bf³i=be²fi, ef³i=efi, bdegi=b⁴egi, bdfgi=b⁴fgi, bfg²i=abce², f³g²i=fg²i, b³ehi=abce, cehi=b²ehi, dehi=adef²h², b³fhi=b³efh, efhi=f²h², f²hi=af²h², fg²hi=b²ce, eh²i=f²h², g²h⁴i=afg²h⁴, b³h⁵i=ab³fh⁵, fh⁵i=ef²h², b²dgh⁵i=b²dfh⁵, h¹⁰i=h⁶i, b³i²=bce², ci²=b²i², di²=df²h², bfi²=abef²h², efi²=af²h², f³i²=fi², bg²i²=bce², eg²i²=b²ce, f²g²i²=g²i², fhi²=f²h², g²hi²=ab²ce, h²i²=f²h², ei³=e²i², fi³=af²i², g²i³=afg²i², i⁴=i²>

P = {a, b², b⁴, c, b²c, ad, ad², b²d², ad³, de, d³e, ae², b²e², b⁴e², ce², b²ce², ade², ad²e², de³, ae⁴, b²e⁴, ce⁴, ade⁴, ad²e⁴, abf, adf, abd²f, ad³f, bef, b³ef, acef, def, bd²ef, d³ef, abe²f, ade²f, abd²e²f, be³f, b³e³f, ace³f, de³f, bd²e³f, abe⁴f, ade⁴f, af², b²f², cf², adf², ad²f², ae²f², abf³, adf³, abd²f³, bef³, acef³, def³, bd²ef³, ab²g, ab⁴g, acg, abdg, ab²d²g, abd³g, ab²e²g, ab⁴e²g, ace²g, abde²g, ab²e⁴g, ace⁴g, dfg, d³fg, cefg, de²fg, ce³fg, de⁴fg, ab²f²g, acf²g, df³g, cef³g, g², e²g², aefg², f²g², eh, ab²eh, ab⁴eh, aceh, bdeh, d²eh, bd³eh, e³h, ab²e³h, bde³h, d²e³h, afh, b²fh, b⁴fh, cfh, b²cfh, abdfh, ad²fh, b²d²fh, abd³fh, ae²fh, b²e²fh, abde²fh, ad²e²fh, ae⁴fh, b²e⁴fh, ad²e⁴fh, ef²h, ab²ef²h, def²h, d²ef²h, af³h, b²f³h, bdf³h, ad²f³h, begh, b⁴egh, be³gh, abfgh, ab⁴fgh, adefgh, ad³efgh, abe²fgh, ade³fgh, abe⁴fgh, bef²gh, ab²f³gh, fg²h, ah², b²h², b⁴h², ch², b²ch², adh², ad²h², b²d²h², ad³h², deh², d³eh², ae²h², b²e²h², ade²h², ad²e²h², de³h², ae⁴h², b²e⁴h², ade⁴h², ad²e⁴h², adfh², ad³fh², efh², ab²efh², ab⁴efh², acefh², defh², d²efh², d³efh², ade²fh², e³fh², ab²e³fh², de³fh², d²e³fh², ade⁴fh², af²h², b²f²h², adf²h², ad²f²h², abgh², ab⁴gh², abdgh², ab²d²gh², abd³gh², abe²gh², abde²gh², abe⁴gh², dfgh², d³fgh², befgh², b⁴efgh², bdefgh², be³fgh², bde³fgh², abf²gh², g²h², ab²h³, ach³, ab²eh³, ab⁴eh³, aceh³, bdeh³, d²eh³, bd³eh³, e³h³, ab²e³h³, bde³h³, d²e³h³, bfh³, b³fh³, bcfh³, b²dfh³, ad²fh³, abd³fh³, ae²fh³, b²e²fh³, abde²fh³, ad²e²fh³, ae⁴fh³, b²e⁴fh³, ad²e⁴fh³, begh³, b⁴egh³, be²gh³, be³gh³, be⁴gh³, afgh³, ab³fgh³, adfgh³, abd²fgh³, ab²e²fgh³, ab²e⁴fgh³, bfg²h³, h⁴, b²h⁴, b⁴h⁴, ch⁴, b²ch⁴, abdh⁴, ad²h⁴, b²d²h⁴, ad³h⁴, d³eh⁴, ae²h⁴, b²e²h⁴, ade²h⁴, ad²e²h⁴, abfh⁴, ad³fh⁴, befh⁴, b³efh⁴, acefh⁴, defh⁴, d²efh⁴, d³efh⁴, ade²fh⁴, ab²gh⁴, ab⁴gh⁴, acgh⁴, ab²d²gh⁴, abd³gh⁴, adegh⁴, abe²gh⁴, cefgh⁴, de²fgh⁴, g²h⁴, adh⁵, eh⁵, ab²eh⁵, deh⁵, d²eh⁵, afh⁵, b²fh⁵, b⁴fh⁵, cfh⁵, adfh⁵, ad²fh⁵, b²d²fh⁵, abd³fh⁵, ae²fh⁵, b²e²fh⁵, dgh⁵, begh⁵, bdegh⁵, abfgh⁵, abdfgh⁵, ad³efgh⁵, abe²fgh⁵, fg²h⁵, ah⁶, b²h⁶, b⁴h⁶, ch⁶, bdh⁶, ad²h⁶, b²d²h⁶, ad³h⁶, ae²h⁶, ad³fh⁶, efh⁶, ab²efh⁶, ab²gh⁶, acgh⁶, abdgh⁶, ab²d²gh⁶, abd³gh⁶, d³fgh⁶, befgh⁶, g²h⁶, eh⁷, ab²eh⁷, deh⁷, afh⁷, b²fh⁷, b⁴fh⁷, cfh⁷, adfh⁷, ad²fh⁷, b²d²fh⁷, abd³fh⁷, begh⁷, abfgh⁷, abdfgh⁷, fg²h⁷, ah⁸, b²h⁸, b⁴h⁸, ch⁸, adh⁸, ad²h⁸, b²d²h⁸, ad³h⁸, ad³fh⁸, abgh⁸, abdgh⁸, ab²d²gh⁸, abd³gh⁸, d³fgh⁸, g²h⁸, ab²h⁹, ach⁹, ab²eh⁹, bfh⁹, b³fh⁹, adfh⁹, b²dfh⁹, ad²fh⁹, abd³fh⁹, egh⁹, b²egh⁹, afgh⁹, abd²fgh⁹, fg²h⁹, h¹⁰, ad²h¹⁰, ad³h¹⁰, ad³fh¹⁰, agh¹⁰, aei, b²ei, b⁴ei, cei, adei, ad²ei, bfi, b³fi, acfi, dfi, bd²fi, be²fi, b³e²fi, de²fi, bd²e²fi, aef²i, b²ef²i, abegi, ab⁴egi, cfgi, efgi, abef²gi, afg²i, ae²fg²i, hi, ab²hi, ab⁴hi, achi, dhi, d²hi, ab²d²hi, d³hi, e²hi, ab²e²hi, bghi, b⁴ghi, bdghi, b²d²ghi, bd³ghi, be²ghi, ag²hi, fh²i, ab²fh²i, acfh²i, dfh²i, d²fh²i, bfgh²i, abh³i, ab³h³i, dh³i, ab²dh³i, d²h³i, d³h³i, b²d³h³i, gh³i, b³gh³i, b²dgh³i, ag²h³i, bfh⁴i, acfh⁴i, dfh⁴i, d²fh⁴i, cfgh⁴i, h⁵i, ab²h⁵i, ach⁵i, dh⁵i, d²h⁵i, ab²d²h⁵i, d³h⁵i, bgh⁵i, bdgh⁵i, bd³gh⁵i, h⁷i, ab²h⁷i, ach⁷i, dh⁷i, d²h⁷i, ab²d²h⁷i, d³h⁷i, bgh⁷i, bdgh⁷i, bd³gh⁷i, abh⁹i, dh⁹i, ab²dh⁹i, d²h⁹i, d³h⁹i, b²d³h⁹i, gh⁹i, ai², b²i², ae²i², b²e²i², af²i², abgi², begi², abe²gi², fgi², ehi², ab²ehi², b²eghi², agi³, hi³, ab²hi³, bghi³}

Phi = 1 a b c d a b e f g h i

Monoid Structure