摘要: A symmetric group action on the maximal chains in a finite, ranked poset is local if adjacent transpositions act such way that $(i,i+1)$ sends each chain either to itself or one differing only at rank $i$. We prove when $S_n$ acts locally lattice, orbit considered as subposet product of chains. also show all posets with actions induced by labellings known $R^* S$-labellings have decompositions and provide for type B D noncrossing partition lattices, answering question Stanley.
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