Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: What power of two divides a weighted Catalan number?   Given a sequence of integers b = (b_0,b_1,b_2,...) one gives a Dyck path P of
length 2n the weight
  wt(P) = b_{h_1} b_{h_2} ... b_{h_n},
  where h_i is the height of the ith ascent of P. The corresponding weighted
Catalan number is
  C_n^b = sum_P wt(P),
  where the sum is over all Dyck paths of length 2n. So, in particular, the
ordinary Catalan numbers C_n correspond to b_i = 1 for all i >= 0. Let xi(n)
stand for the base two exponent of n, i.e., the largest power of 2 dividing n.
We give a condition on b which implies that
  xi(C_n^b) = xi(C_n).
  In the special case b_i=(2i+1)^2, this settles a conjecture of Postnikov
about the number of plane Morse links. Our proof generalizes the recent
combinatorial proof of Deutsch and Sagan of the classical formula for xi(C_n).

9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
16
The categories of this paper are: stat
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom