Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bijective enumerations of $\Gamma$-free 0-1 matrices   We construct a new bijection between the set of $n\times k$ $0$-$1$ matrices
with no three $1$'s forming a $\Gamma$ configuration and the set of
$(n,k)$-Callan sequences, a simple structure counted by poly-Bernoulli numbers.
We give two applications of this result: We derive the generating function of
$\Gamma$-free matrices, and we give a new bijective proof for an elegant result
of Aval et al. that states that the number of complete non-ambiguous forests
with $n$ leaves is equal to the number of pairs of permutations of
$\{1,\dots,n\}$ with no common rise.

15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci