Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Logarithmic Tree Factorials   To any rooted tree, we associate a sequence of numbers that we call the
logarithmic factorials of the tree. This provides a generalization of
Bhargava's factorials to a natural combinatorial setting suitable for studying
questions around generalized factorials.
  We discuss several basic aspects of the framework in this paper. In
particular, we relate the growth of the sequence of logarithmic factorials
associated to a tree to the transience of the random walk and the existence of
a harmonic measure on the tree, obtain an equidistribution theorem for
factorial-determining-sequences of subsets of local fields, and provide a
factorial-based characterization of the branching number of infinite trees.
  Our treatment is based on a local weighting process in the tree which gives
an effective way of constructing the factorial sequence.

18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con