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- W2949062464 abstract "Let $(W,S)$ be an arbitrary Coxeter system. For each word $omega$ in the generators we define a partial order--called the {sf $omega$-sorting order}--on the set of group elements $W_omegasubseteq W$ that occur as subwords of $omega$. We show that the $omega$-sorting order is a supersolvable join-distributive and that it is strictly between the weak and Bruhat orders on the group. Moreover, the $omega$-sorting order is a maximal lattice in the sense that the addition of any collection of Bruhat covers results in a nonlattice. Along the way we define a class of structures called {sf supersolvable antimatroids} and we show that these are equivalent to the class of supersolvable join-distributive lattices." @default.
- W2949062464 created "2019-06-27" @default.
- W2949062464 creator A5003392168 @default.
- W2949062464 date "2007-12-07" @default.
- W2949062464 modified "2023-09-27" @default.
- W2949062464 title "The sorting order on a Coxeter group" @default.
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