Miller, Alexander R. Differential posets have strict rank growth: a conjecture of Stanley. (English) Zbl 1283.06006 Order 30, No. 2, 657-662 (2013). 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. Cited in 4 Documents MSC: 06A07 Combinatorics of partially ordered sets Keywords:Smith normal forms; differential posets; strict growth PDF BibTeX XML Cite \textit{A. R. Miller}, Order 30, No. 2, 657--662 (2013; Zbl 1283.06006) Full Text: DOI arXiv References: [1] Brouwer, A.E., Haemers, W.H.: Spectra of Graphs. Springer (2012) · Zbl 1231.05001 [2] Miller, AR; Reiner, V, Differential posets and Smith normal forms, Order, 26, 197-228, (2009) · Zbl 1228.05096 [3] Stanley, RP, Differential posets, J. Am. Math. Soc., 1, 919-961, (1988) · Zbl 0658.05006 [4] Stanley, RP; Zanello, F, On the rank function of a differential poset, Electronic J. Combinatorics, 19, 13, (2012) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.