#354 ⟨a, b | aaaabba=b⟩

Up:Monoid enumeration
Prev:#353 ⟨a, b | aaaabba=a⟩
Next:#355 ⟨a, b | aaaabbb=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. a4b3 ⇒ ba3b2a [2]
2. a4b2a ⇒ b [1]
# ab:aaaabba=b ba - -
aaaabbb=baaabba
aaaabba=b

Other submonoids of same group

6 unique, 11 total

Σ#PresentationPropertiesφ
8423⟨a, b | aaaaba=bb⟩Can Inf
91022⟨a, b | aaaaba=bab⟩Can Inf
102398⟨a, b | aaaaba=baab⟩Can Inf
113068⟨a, b | aababababba=1⟩Grp Inf5
113771⟨a, b | ababababba=b⟩Can Inf
115486⟨a, b | aaaaba=baaab⟩Can Inf

Other submonoids of anti-isomorphic group

3 unique, 3 total

Σ#PresentationProperties
9752⟨a, b | aaaababa=b⟩Can Inf
101584⟨a, b | aaaabaaba=b⟩Can Inf
113371⟨a, b | aaaabaaaba=b⟩Can Inf