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Peckness of Edge Posets

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Abstract

For any graded poset P, we define a new graded poset, 𝓔(P), whose elements are the edges in the Hasse diagram of P. For any group G acting on the boolean algebra B n in a rank-preserving fashion we conjecture that 𝓔(B n /G) is Peck. We prove that the conjecture holds for “common cover transitive” actions. We give some infinite families of common cover transitive actions and show that the common cover transitive actions are closed under direct and semidirect products.

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Authors and Affiliations

  1. Duke University, 6300 Lakeland Dr., Raleigh, NC, 27612, USA

    David Hemminger

  2. Harvard University, 323 Eliot Mail Center, Cambridge, MA, 02138, USA

    Aaron Landesman

  3. Brown University, 7285 Brown University, Providence, RI, 02912, USA

    Zijian Yao

Authors
  1. David Hemminger
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  2. Aaron Landesman
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  3. Zijian Yao
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Correspondence to David Hemminger.

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Hemminger, D., Landesman, A. & Yao, Z. Peckness of Edge Posets. Order 34, 441–463 (2017). https://doi.org/10.1007/s11083-016-9408-x

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  • DOI: https://doi.org/10.1007/s11083-016-9408-x

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