A characterization of 3+1free posets
Mark Skandera
MIT
May 5,
4:15pm
refreshments at 3:45pm
2338
ABSTRACT

Posets containing no subposet isomorphic to the disjoint
sums of chains $\mathbf{3+1}$ and/or $\mathbf{2+2}$ are known to have
many special properties.
However, while
posets free of $\mathbf{2+2}$ and posets free of
both $\mathbf{2+2}$ and $\mathbf{3+1}$ may
be characterized as interval orders, no such characterization is known
for posets free only of $\mathbf{3+1}$.
We give a characterization of
$(\mathbf{3+1})$free posets in terms of their antiadjacency matrices.
Using results about totally positive matrices, we show that this
characterization leads to a simple proof that the chain polynomial
of a $(\mathbf{3+1})$free poset has only real zeros.

Speaker's Contact Info: skan(atsign)math.mit.edu
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