Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linearization of monomial ideals   We introduce a construction, called linearization, that associates to any
monomial ideal $I$ an ideal $\mathrm{Lin}(I)$ in a larger polynomial ring. The
main feature of this construction is that the new ideal $\mathrm{Lin}(I)$ has
linear quotients. In particular, since $\mathrm{Lin}(I)$ is generated in a
single degree, it follows that $\mathrm{Lin}(I)$ has a linear resolution. We
investigate some properties of this construction, such as its interplay with
classical operations on ideals, its Betti numbers, functoriality and
combinatorial interpretations. We moreover introduce an auxiliary construction,
called equification, that associates to any monomial ideal a new monomial ideal
generated in a single degree, in a polynomial ring with one more variable. We
study some of the homological and combinatorial properties of the equification,
which can be seen as a monomial analogue of the well-known homogenization
construction.

7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph