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The ***h*^{*}-Polynomial of the Cut Polytope
of *K*_{2,m} in the Lattice Spanned by its Vertices

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Ryuichi Sakamoto

Department of Mathematical Sciences

Graduate School of Science and Technology

Kwansei Gakuin University

Sanda, Hyogo 669-1337

Japan

**Abstract:**

The cut polytope of a graph is an important object in several fields, such
as functional analysis, combinatorial optimization, and probability. For
example, Sturmfels and Sullivant showed that the toric ideals of cut
polytopes are useful in algebraic statistics. In the theory of lattice
polytopes, the *h*^{*}-polynomial is an important invariant. However, except
for trees, there are no classes of graphs for which the *h*^{*}-polynomial
of their cut polytope is explicitly specified. In the present paper,
we determine the *h*^{*}-polynomial of the cut polytope of the complete
bipartite graph *K*_{2,m} using the theory of Gröbner bases of toric ideals.

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Received June 12 2019; revised versions received July 5 2019; September 26 2019; September 28 2019; April 9 2020.
Published in *Journal of Integer Sequences*,
June 27 2020.

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