Geodesic
Deformation of chains via a local symmetric group action
The electronic journal of combinatorics, Tome 6 (1999)
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A symmetric group action on the maximal chains in a finite, ranked poset is local if the adjacent transpositions act in such a way that $(i,i+1)$ sends each maximal chain either to itself or to one differing only at rank $i$. We prove that when $S_n$ acts locally on a lattice, each orbit considered as a subposet is a product of chains. We also show that all posets with local actions induced by labellings known as $R^* S$-labellings have symmetric chain decompositions and provide $R^* S$-labellings for the type B and D noncrossing partition lattices, answering a question of Stanley.
DOI : 10.37236/1459
Classification : 06A07
Mots-clés : local action, orbit, maximal chain, symmetric group, partition lattice 
@article{10_37236_1459,
     author = {Patricia Hersh},
     title = {Deformation of chains via a local symmetric group action},
     journal = {The electronic journal of combinatorics},
     year = {1999},
     volume = {6},
     doi = {10.37236/1459},
     zbl = {0921.05062},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1459/}
}
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Patricia Hersh. Deformation of chains via a local symmetric group action. The electronic journal of combinatorics, Tome 6 (1999). doi: 10.37236/1459

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