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• W2013016810 abstract "Let L be a lattice admitting a left-modular chain of length r, not necessarily maximal. We show that if either L is graded or the chain is modular, then the (r-2)-skeleton of L is vertex-decomposable (hence shellable). This proves a conjecture of Hersh. Under certain circumstances, we can find shellings of higher skeleta. For instance, if the left-modular chain consists of every other element of some maximum length chain, then L itself is shellable. We apply these results to give a new characterization of finite solvable groups in terms of the topology of subgroup lattices. Our main tool relaxes the conditions for an EL-labeling, allowing multiple ascending chains as long as they are lexicographically before non-ascending chains. We extend results from the theory of EL-shellable posets to such labelings. The shellability of certain skeleta is one such result. Another is that a poset with such a labeling is homotopy equivalent (by discrete Morse theory) to a cell complex with cells in correspondence to weakly descending chains." @default.
• W2013016810 created "2016-06-24" @default.
• W2013016810 creator A5057457874 @default.
• W2013016810 date "2012-08-01" @default.
• W2013016810 modified "2023-10-18" @default.
• W2013016810 title "Chains of modular elements and shellability" @default.
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• W2013016810 doi "https://doi.org/10.1016/j.jcta.2012.03.009" @default.
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