×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
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.