Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting Bipartite, k-Colored and Directed Acyclic Multi Graphs Through
  F-nomial coefficients   F-nomial coefficients encompass among others well-known binomial coefficients
or Gaussian coefficients that count subsets of finite set and subspaces of
finite vector space respectively. Here, the so called F-cobweb tiling sequences
N(a) are considered. For such specific sequences a new interpretation with
respect to Kwasniewski general combinatorial interpretation of F-nomial
coefficients is unearhed.
  Namely, for tiling sequences F = N(a)$ the F-nomial coefficients are equal to
the number of labeled special bipartite multigraphs denoted here as
a-multigraphs G(a,n,k).
  An explicit relation between the number of k-colored a-multigraphs and multi
N(a)-nomial coefficients is established. We also prove that the unsigned values
of the first row of inversion matrix for N(a) -nomial coefficients considered
here are equal to the numbers of directed acyclic a-multigraphs with n nodes.

11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat