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Path Counting and Rank Gaps in Differential Posets

Author(s)
Gaetz, Christian; Venkataramana, Praveen
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Abstract
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.
Date issued
2019-09-21
URI
https://hdl.handle.net/1721.1/131754
Publisher
Springer Netherlands
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