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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.

##### MSC:
 06A07 Combinatorics of partially ordered sets
##### Keywords:
Smith normal forms; differential posets; strict growth
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##### 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)
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