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Differential posets have strict rank growth: a conjecture of Stanley. (English) Zbl 1283.06006
Summary: We establish strict growth for the rank function of an \(r\)-differential poset. We do so by exploiting the representation-theoretic techniques developed by V. Reiner and the author [Order 26, No. 3, 197–228 (2009; Zbl 1228.05096)] for studying related Smith forms.

06A07 Combinatorics of partially ordered sets
Full Text: DOI arXiv
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[2] Miller, AR; Reiner, V, Differential posets and Smith normal forms, Order, 26, 197-228, (2009) · Zbl 1228.05096
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[4] Stanley, RP; Zanello, F, On the rank function of a differential poset, Electronic J. Combinatorics, 19, 13, (2012)
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