Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ehrhart Theory of Paving and Panhandle Matroids   We show that the base polytope $P_M$ of any paving matroid $M$ can be
obtained from a hypersimplex by slicing off subpolytopes. The pieces removed
are base polytopes of lattice path matroids corresponding to panhandle-shaped
Ferrers diagrams, whose Ehrhart polynomials we can calculate explicitly.
Consequently, we can write down the Ehrhart polynomial of $P_M$, starting with
Katzman's formula for the Ehrhart polynomial of a hypersimplex. The method
builds on and generalizes Ferroni's work on sparse paving matroids.
Combinatorially, our construction corresponds to constructing a uniform matroid
from a paving matroid by iterating the operation of stressed-hyperplane
relaxation introduced by Ferroni, Nasr, and Vecchi, which generalizes the
standard matroid-theoretic notion of circuit-hyperplane relaxation. We present
evidence that panhandle matroids are Ehrhart positive and describe a
conjectured combinatorial formula involving chain gangs and Eulerian numbers
from which Ehrhart positivity of panhandle matroids will follow. As an
application of the main result, we calculate the Ehrhart polynomials of
matroids associated with Steiner systems and finite projective planes, and show
that they depend only on their design-theoretic parameters: for example, while
projective planes of the same order need not have isomorphic matroids, their
base polytopes must be Ehrhart equivalent.

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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg