Equivariant lattice bases

IF 1.2 2区数学 Q1 MATHEMATICS Transactions of the American Mathematical Society Pub Date : 2024-04-19 DOI:10.1090/tran/9193

Dinh Le, Tim Römer

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引用次数: 0

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 Z ( N × [ c ] ) \mathbb {Z}^{(\mathbb {N}\times [c])} , where c ∈ N c\in \mathbb {N} , has a finite equivariant Graver basis. This result generalizes and strengthens several finiteness results about Markov bases in the literature.

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等变乳胶基

我们研究在无限对称群作用下不变的无限秩自由无边群中的网格，重点是其等变基的有限性。我们的框架为证明代数统计中的有限性结果提供了一种新方法。举例来说，我们证明了 Z ( N × [ c ] ) 中的每一个不变网格都是\mathbb {Z}^{(\mathbb {N}\times [c])} 。其中 c ∈ N c\in \mathbb {N}, 有一个有限等变格雷弗基。这一结果概括并加强了文献中关于马尔可夫基的几个有限性结果。

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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.

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