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$begingroup$

I'm trying to get a list of all words of length $n$ (in the word metric sense) in some finitely presented group. I have tried some very naive enumerations but it is very slow. Is there an efficient way of doing this?

gap finitely-generated sagemath cayley-graphs

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edited Mar 12 at 23:16

Alexander Konovalov

5,24221957

asked Mar 12 at 14:22

UP_TLVUP_TLV

114

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Do you care about different words, or different elements (I.e. a shortest word?) for what kind of group?
  $endgroup$
  – ahulpke
  Mar 13 at 8:35
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  A discrete subgroup of SL2R generated by 2 elements with some relations between them. I'm interested in reduced words only (A^2A^-1 has length 1 for example).
  $endgroup$
  – UP_TLV
  Mar 14 at 10:14
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  In other words, take the Cayley graph with the obvious graph metric, and compute the ball of size n.
  $endgroup$
  – UP_TLV
  Mar 14 at 10:15
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  If you know matrix images of your generators, you could form words of increasing length systematically and discard if the evaluated images are equal. Otherwise, unless you happen to be able to have a confluent rewriting system, I doubt there is a better method.
  $endgroup$
  – ahulpke
  Mar 16 at 6:40
  

  
  
  
  

add a comment | 

0

$begingroup$

I'm trying to get a list of all words of length $n$ (in the word metric sense) in some finitely presented group. I have tried some very naive enumerations but it is very slow. Is there an efficient way of doing this?

gap finitely-generated sagemath cayley-graphs

share|cite|improve this question

edited Mar 12 at 23:16

Alexander Konovalov

5,24221957

asked Mar 12 at 14:22

UP_TLVUP_TLV

114

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Do you care about different words, or different elements (I.e. a shortest word?) for what kind of group?
  $endgroup$
  – ahulpke
  Mar 13 at 8:35
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  A discrete subgroup of SL2R generated by 2 elements with some relations between them. I'm interested in reduced words only (A^2A^-1 has length 1 for example).
  $endgroup$
  – UP_TLV
  Mar 14 at 10:14
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  In other words, take the Cayley graph with the obvious graph metric, and compute the ball of size n.
  $endgroup$
  – UP_TLV
  Mar 14 at 10:15
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  If you know matrix images of your generators, you could form words of increasing length systematically and discard if the evaluated images are equal. Otherwise, unless you happen to be able to have a confluent rewriting system, I doubt there is a better method.
  $endgroup$
  – ahulpke
  Mar 16 at 6:40
  

  
  
  
  

add a comment | 

$begingroup$

I'm trying to get a list of all words of length $n$ (in the word metric sense) in some finitely presented group. I have tried some very naive enumerations but it is very slow. Is there an efficient way of doing this?

gap finitely-generated sagemath cayley-graphs

share|cite|improve this question

edited Mar 12 at 23:16

Alexander Konovalov

5,24221957

asked Mar 12 at 14:22

UP_TLVUP_TLV

114

$endgroup$

share|cite|improve this question

edited Mar 12 at 23:16

Alexander Konovalov

5,24221957

asked Mar 12 at 14:22

UP_TLVUP_TLV

114

share|cite|improve this question

edited Mar 12 at 23:16

Alexander Konovalov

5,24221957

asked Mar 12 at 14:22

UP_TLVUP_TLV

114

edited Mar 12 at 23:16

Alexander Konovalov

5,24221957

edited Mar 12 at 23:16

Alexander Konovalov

5,24221957

asked Mar 12 at 14:22

UP_TLVUP_TLV

114

asked Mar 12 at 14:22

UP_TLVUP_TLV

114