Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic and combinatorial properties of ideals and algebras of uniform
  clutters of TDI systems   Let C be a uniform clutter, i.e., all the edges of C have the same size, and
let A be the incidence matrix of C. We denote the column vectors of A by
v1,...,vq. The vertex covering number of C, denoted by g, is the smallest
number of vertices in any minimal vertex cover of C. Under certain conditions
we prove that C is vertex critical. If C satisfies the max-flow min-cut
property, we prove that A diagonalizes over the integers to an identity matrix
and that v1,...,vq is a Hilbert basis. It is shown that if C has a perfect
matching such that C has the packing property and g=2, then A diagonalizes over
the integers to an identity matrix. If A is a balanced matrix we prove that any
regular triangulation of the cone generated by v1,...,vq is unimodular. Some
examples are presented to show that our results only hold for uniform clutters.
These results are closely related to certain algebraic properties, such as the
normality or torsion freeness, of blowup algebras of edge ideals and to
finitely generated abelian groups. They are also related to the theory of
Gr\"obner bases of toric ideals and to Ehrhart rings.

18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg