An r-uniform hypergraph H consists of a set of vertices V and a set of edges whose elements are r-subsets of V. We define a hypertree to be a connected hypergraph which contains no cycles. A hypertree spans a hypergraph H
Nearby in the stack
if it is a subhypergraph of
H
which contains all vertices of
H
. Greenhill, Isaev, Kwan and McKay (2017) gave an asymptotic formula for the average number of spanning trees in graphs with given, sparse degree sequence. We prove an analogous result for
r
-uniform hypergraphs with given degree sequence
k=(k1,…,kn)
. Our formula holds when
r5kmax3=o((kr−k−r)n)
, where
k
is the average degree and
kmax
is the maximum degree.
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