Hermite Normal Forms and Δ-vector
نویسندگان
چکیده
Let δ(P) = (δ0, δ1, . . . , δd) be the δ-vector of an integral polytope P ⊂ R of dimension d. Following the previous work of characterizing the δvectors with ∑d i=0 δi ≤ 3, the possible δ-vectors with ∑d i=0 δi = 4 will be classified. And each possible δ-vectors can be obtained by simplices. We get this result by studying the problem of classifying the possible integral simplices with a given δ-vector (δ0, δ1, . . . , δd), where ∑d i=0 δi ≤ 4, by means of Hermite normal forms of square matrices.
منابع مشابه
Classification of Ehrhart polynomials of integral simplices
Let δ(P) = (δ0, δ1, . . . , δd) be the δ-vector of an integral convex polytope P of dimension d. First, by using two well-known inequalities on δ-vectors, we classify the possible δ-vectors with ∑d i=0 δi ≤ 3. Moreover, by means of Hermite normal forms of square matrices, we also classify the possible δ-vectors with ∑d i=0 δi = 4. In addition, for ∑d i=0 δi ≥ 5, we characterize the δ-vectors of...
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