Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On optimizing discrete Morse functions   Forman introduced discrete Morse theory as a tool for studying CW complexes
by essentially collapsing them onto smaller, simpler-to-understand complexes of
critical cells in [Fo]. Chari reformulated discrete Morse theory for regular
cell complexes in terms of acyclic matchings on face posets in [Ch]. This paper
addresses two questions: (1) under what conditions may several gradient paths
in a discrete Morse function simultaneously be reversed to cancel several pairs
of critical cells, to further collapse the complex, and (2) how to use
lexicographically first reduced expressions for permutations (in the sense of
[Ed]) to make (1) practical for poset order complexes.
  Applications include Cohen-Macaulayness of a new partial order, recently
introduced by Remmel, on the symmetric group (by refinement on the underlying
partitions into cycles) as well as a simple new proof of the homotopy type for
intervals in the weak order for the symmetric group. Additional applications
appear in [HW].

30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th