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Differential Posets have Strict Rank Growth: A Conjecture of Stanley

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Abstract

We establish strict growth for the rank function of an r-differential poset. We do so by exploiting the representation theoretic techniques developed by Reiner and the author (Order 26(3):197–228, 2009) for studying related Smith forms.

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References

  1. Brouwer, A.E., Haemers, W.H.: Spectra of Graphs. Springer (2012)

  2. Miller, A.R., Reiner, V.: Differential posets and Smith normal forms. Order 26(3), 197–228 (2009)

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  3. Stanley, R.P.: Differential posets. J. Am. Math. Soc. 1, 919–961 (1988)

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  4. Stanley, R.P., Zanello, F.: On the rank function of a differential poset. Electronic J. Combinatorics 19(2), 13 (2012)

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Alexander R. Miller

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  1. Alexander R. Miller
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Correspondence to Alexander R. Miller.

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Supported by NSF grant DMS-1001933.

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Miller, A.R. Differential Posets have Strict Rank Growth: A Conjecture of Stanley. Order 30, 657–662 (2013). https://doi.org/10.1007/s11083-012-9268-y

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  • DOI: https://doi.org/10.1007/s11083-012-9268-y

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