Timeline for Adding a formal inverse of an element to a free monoid
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Sep 17, 2020 at 10:03 | comment | added | Carl-Fredrik Nyberg Brodda | Just for the record: this is really just Adian's algorithm for computing the invertible pieces of a one-relator special monoid. | |
| Mar 14, 2011 at 14:43 | comment | added | ADL |
I know you said you do not want examples, but the primitive pairs in $F(a, b)$ where $a$ and $b$ only occur with positive exponent work', as can be seen from your algorithm (i.e. if $<u, v> = F(a, b)$ and $u, v \in S_i$ for some $i$ then your word works). Thus, for example, $W=uvu$ works. The primitive pairs work because your algorithm can be used to unpick' the automorphisms $a\mapsto ab, b\mapsto b$, $a\mapsto ba, b\mapsto b$, and $a\mapsto b, b\mapsto a$ of $F(a, b)$. Also, I am unsure how one would gain a complete description; if $W$ works then so does, for example, $W^iUW^j$ for all $U$
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| Mar 14, 2011 at 11:52 | vote | accept | CommunityBot | moved from User.Id=6976 by developer User.Id=69903 | |
| Mar 14, 2011 at 11:52 | vote | accept | CommunityBot | moved from User.Id=6976 by developer User.Id=69903 | |
| Mar 14, 2011 at 11:52 | |||||
| Mar 14, 2011 at 3:47 | history | answered | user6976 | CC BY-SA 2.5 |