Spanning trees in complete uniform hypergraphs and a connection to extended r-Shi hyperplane arrangements

Details Spanning trees in complete uniform hypergraphs and a connection to extended r-Shi hyperplane arrangements Spanning trees in complete uniform hypergraphs and a connection to extended r-Shi hyperplane arrangements

2006-05-03

arxiv.org/abs/math/0605083v2

Mathematics

Combinatorics

11 pages, 5 figures, corrected scores of errors, added a section on gen fns

Scientific paper

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 and r-Parking functions. We observe a simple consequence of this bijection in terms of the number of regions of the extended Shi arrangement.

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