Timeline for Number of occurrences of certain generators in expressions in Coxeter groups
Current License: CC BY-SA 3.0
4 events
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| Jul 20, 2017 at 18:38 | comment | added | Gro-Tsen | @SamHopkins Let $\bar w$ be any expression for $w$ with $m_I(w)$ generators from $I$. Then (Björner & Brenti, corollary 1.4.8(i)) there is a subword $\bar w'$ of $\bar w$ (in the sense that some letters have been removed from $\bar w$) that is a reduced expression for $w$; but the number of generators from $I$ cannot have decreased, by minimality of $m_I(w)$, so $\bar w'$ is a reduced expression for $w$ with $m_I(w)$ generators from $I$. | |
| Jul 20, 2017 at 17:53 | comment | added | Sam Hopkins | Is your assertion about $m_I(w)$ being realized by a reduced expression for $w$ clear? | |
| Jul 20, 2017 at 17:18 | history | edited | YCor |
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| Jul 20, 2017 at 16:17 | history | asked | Gro-Tsen | CC BY-SA 3.0 |