Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal generating degrees of powers of homogeneous ideals   The degree excess function $\epsilon(I;n)$ is the difference between the
maximal generating degree $d(I^n)$ of a homogeneous ideal $I$ of a polynomial
ring and $p(I)n$, where $p(I)$ is the leading coefficient of the asymptotically
linear function $d(I^n)$. It is shown that any non-increasing numerical
function can be realized as a degree excess function, and there is a monomial
ideal $I$ whose $\epsilon(I;n)$ has exactly a given number of local maxima. In
the case of monomial ideals, an upper bound on $\epsilon(I;n)$ is provided. As
an application it is shown that in the worst case, the so-called stability
index of the Castelnuovo-Mumford regularity of a monomial ideal $I$ must be at
least an exponential function of the number of variables.

14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con