Path Counting and Rank Gaps in Differential Posets
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11083_2019_9504_ReferencePDF.pdf
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Author(s)
Gaetz, Christian
Venkataramana, Praveen
Date Issued
September 2019
Publisher
Springer Netherlands
Version
Author's final manuscript
Abstract
We study the gaps Δpn between consecutive rank sizes in r-differential posets by introducing a projection operator whose matrix entries can be expressed in terms of the number of certain paths in the Hasse diagram. We strengthen Miller’s result that Δpn ≥ 1, which resolved a longstanding conjecture of Stanley, by showing that Δpn ≥ 2r. We also obtain stronger bounds in the case that the poset has many substructures called threads.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s11083-019-09504-4
