Spanning trees in complete uniform hypergraphs and a connection to r-extended Shi hyperplane arrangements
نویسنده
چکیده
We give a Cayley type formula to count the number of spanning trees in the complete r-uniform hypergraph for all r ≥ 3. Similar to the bijection between spanning trees of the complete graph on (n + 1) vertices and Parking functions of length n, we derive a bijection from spanning trees of the complete (r + 1)-uniform hypergraph which arise from a fixed r-perfect matching (see Section 2) and r-Parking functions of an appropriate length. We observe a simple consequence of this bijection in terms of the number of regions of the r-extended Shi hyperplane arrangement in n dimensions, S n.
منابع مشابه
Spanning trees in complete uniform hypergraphs and a connection to extended Shi hyperplane arrangements
We give a Cayley type formula to count the number of spanning trees in the complete r-uniform hypergraph for all r ≥ 3. Similar to the bijection between spanning trees in complete graphs and Parking functions, we derive a bijection from spanning trees of the complete (r + 1)-uniform hypergraph which arise from a fixed r-perfect matching (see Section 2) and r-Parking functions. We observe a simp...
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