#863 ⟨a, b | abbabbba=b⟩

Up:Monoid enumeration
Prev:#862 ⟨a, b | abbabbba=a⟩
Next:#864 ⟨a, b | abbbaaab=a⟩

Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic 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. ab2ab4 ⇒ (b3a)2 [2]
2. ab2ab3a ⇒ b [1]
# ab:abbabbba=b ba - -
abbabbbb=bbbabbba
abbabbba=b

Other submonoids of same group

6 unique, 25 total

Σ#PresentationPropertiesφ
7254⟨a, b | aaba=bbb⟩Can Inf
8290⟨a, b | aaababba=1⟩Grp Inf19
8478⟨a, b | ababba=bb⟩Can Inf
91263⟨a, b | ababa=babb⟩Can Inf
114796⟨a, b | abaababa=bab⟩Can Inf
115405⟨a, b | abbabba=babb⟩Can Inf

Other submonoids of anti-isomorphic group

3 unique, 3 total

Σ#PresentationProperties
7186⟨a, b | aabbba=b⟩Can Inf
9804⟨a, b | aabababa=b⟩Can Inf
113560⟨a, b | aabaabaaba=b⟩Can Inf