# Joshua Swanson: DUSTPAN distributions as limit laws for Mahonian statistics on forests

**Tuesday, December 15th, at 10.15 **

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https://uni-lj-si.zoom.us/j/97829064282?pwd=Q2JQZWFjV0pMNjJaM1YwK016Q2FHdz09

Meeting ID: 978 2906 4282

Passcode: 643844

**Abstract. **Building on work of Stanley and
Björner–Wachs, we study the distribution of certain Mahonian statistics
on several families of posets, including the major index on linear
extensions of forests. We show that the resulting standardized
distributions are often asymptotically normal. However, in certain
regimes, we must introduce a new, closed family of continuous
probability distributions called DUSTPAN distributions which
simultaneously generalize the Irwin–Hall and normal distributions. In
the case of forests, we use graph-theoretic statistics like height and
elevation to completely determine the precise limit laws. This leads to
some natural open questions about the distribution of the height of such
forests.

Joint work with Sara Billey (https://arxiv.org/abs/2010.12701)

building on earlier joint work with Sara Billey and Matjaž Konvalinka (https://arxiv.org/abs/1905.00975).