Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Degree and regularity of vanishing ideals of algebraic toric sets
  over finite fields   Let X* be a subset of an affine space A^s, over a finite field K, which is
parameterized by the edges of a clutter. Let X and Y be the images of X* under
the maps x --> [x] and x --> [(x,1)] respectively, where [x] and [(x,1)] are
points in the projective spaces P^{s-1} and P^s respectively. For certain
clutters and for connected graphs, we were able to relate the algebraic
invariants and properties of the vanishing ideals I(X) and I(Y). In a number of
interesting cases, we compute its degree and regularity. For Hamiltonian
bipartite graphs, we show the Eisenbud-Goto regularity conjecture. We give
optimal bounds for the regularity when the graph is bipartite. It is shown that
X* is an affine torus if and only if I(Y) is a complete intersection. We
present some applications to coding theory and show some bounds for the minimum
distance of parameterized linear codes for connected bipartite graphs.

35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con