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The h, k-equal Partition Lattice is EL-shellable when h \(\geq\) k

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Abstract

It has been shown that the h, k-equal partition lattice \(\tilde \Pi_n^{h, k}\) is EL-shellable when h < k. We produce an EL-shelling for \(\tilde \Pi_n^{h, k}\) when n ≥ h ≥ k ≥ 2 and observe that, in this shelling, there are no weakly decreasing chains. This shows that \(\tilde \Pi_n^{h, k}\) is contractible for such values of h and k, which can also be seen by the fact that \(\tilde \Pi_n^{h, k}\) is noncomplemented.

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  1. Department of Mathematics and Computer Science, Rhodes College, 2000 N. Parkway, Memphis, TN, 38112-1690, USA

    Eric Gottlieb

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  1. Eric Gottlieb
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Correspondence to Eric Gottlieb.

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In memory of Frank and Gloria Heller and their remarkable optimism.

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Gottlieb, E. The h, k-equal Partition Lattice is EL-shellable when h \(\geq\) k . Order 31, 259–269 (2014). https://doi.org/10.1007/s11083-013-9299-z

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