Fibonacci Polytopes and Their Applications
نویسنده
چکیده
A Fibonacci d-polytope of order k is defined as the convex hull of {0, 1}-vectors with d entries and no consecutive k ones, where k ≤ d. We show that these vertices can be partitioned into k subsets such that the convex hull of the subsets give the equivalent of Fibonacci (d− i)polytopes, for i = 1, . . . , k, which yields a “Fibonacci like” recursive formula to enumerate the vertices. Surprisingly, the polytopes are totally unimodular and require a small number of inequalities to describe them. These facts are used to enumerate compositions of a positive integer with bounded summands, and to find various compositions.
منابع مشابه
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