Year: 2023
Type: preprint
Abstract: We study lattices in free abelian groups of infinite rank that are invariant under the action of the infinite symmetric group, with emphasis on finiteness of their equivariant bases. Our framework provides a new method for proving finiteness results in algebraic statistics. As an illustration, we show that every invariant lattice in $\mathbb{Z}^{(\mathbb{N}\times[c])}$, where $c\in\mathbb{N}$, has a finite equivariant Graver basis. This result generalizes and strengthens several finiteness results about Markov bases in the literature.
Source: arXiv (Cornell University)
Authors: Van Le, Dinh, Römer, Tim
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4386807896