#268 ⟨a, b | abba=bbb⟩

Up:Monoid enumeration
Prev:#267 ⟨a, b | abba=bab⟩
Next:#269 ⟨a, b | aaaaaaaa=1⟩

Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group

Properties

Rewriting system

Format:
Word:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 1 
1
#RuleProof
1. ab2a ⇒ b3 [1]
2. b5a ⇒ ab5 [2]
# ab:abba=bbb ab - -
abba=bbb
bbbbba=abbbbb

Other submonoids of same group

7 unique, 18 total

Σ#PresentationPropertiesφ
7131⟨a, b | aaaabba=1⟩Grp Inf11
7196⟨a, b | abbbba=b⟩Can Inf
7199⟨a, b | aaaaa=bb⟩Can Inf
7232⟨a, b | abbba=bb⟩Can Inf
7237⟨a, b | aaaa=bab⟩Can Inf
102333⟨a, b | abababa=bab⟩Can Inf
102767⟨a, b | babab=ababa⟩Can Inf