Spanning trees in complete uniform hypergraphs and a connection to extended r-Shi hyperplane arrangements
Combinatorics
2007-05-23 v2
Abstract
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.
Cite
@article{arxiv.math/0605083,
title = {Spanning trees in complete uniform hypergraphs and a connection to extended r-Shi hyperplane arrangements},
author = {Sivaramakrishnan Sivasubramanian},
journal= {arXiv preprint arXiv:math/0605083},
year = {2007}
}
Comments
11 pages, 5 figures, corrected scores of errors, added a section on gen fns