Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On common divisors of multinomial coefficients   Erd\H{o}s and Szekeres showed in 1978 that for any four positive integers
satisfying m_1+m_2 = n_1+n_2, the two binomial coefficients (m_1+m_2)!/m_1!
m_2! and (n_1+n_2)!/n_1! n_2! have a common divisor >1. The analogous statement
for families of k k-nomial coefficients (k>1) was conjectured in 1997 by David
Wasserman.
  Erd\H{o}s and Szekeres remark that if m_1, m_2, n_1, n_2 as above are all >1,
there is probably a lower bound on the common divisor in question which goes to
infinity as a function of m_1+m_2. Such a bound is here obtained.
  Results are proved that narrow the class of possible counterexamples to
Wasserman's conjecture. On the other hand, several plausible generalizations of
that conjecture are shown to be false.

25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph