Minimal free resolutions of 2 x n domino tilings

Bouchat Rachelle R.; Brown Tricia Muldoon

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Minimal free resolutions of 2 x n domino tilings

机译：最小的自由分辨率为2 x N Domino Tilings

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摘要

We introduce a squarefree monomial ideal associated to the set of domino tilings of a 2 x n rectangle and proceed to study the associated minimal free resolution. In this paper, we use results of Dalili and Kummini to show that the Betti numbers of the ideal are independent of the underlying characteristic of the field, and apply a natural splitting to explicitly determine the projective dimension and Castelnuovo-Mumford regularity of the ideal.

机译：我们介绍了与2×N矩形的Domino倾斜组相关的SquareFree单体理想，并继续研究相关的最小自由分辨率。在本文中，我们使用Dalili和Kummini的结果表明，理想的贝蒂数量独立于该领域的潜在特征，并应用自然分裂以明确地确定理想的投影维度和Castelnuovo-Mumford规律。

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来源
《Journal of algebra and its applications》 |2019年第6期|共16页
作者
Bouchat Rachelle R.; Brown Tricia Muldoon;
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作者单位

Indiana Univ Penn Dept Math 1011 South Dr Indiana PA 15705 USA;

Georgia Southern Univ Dept Math Armstrong Campus 11935 Abercorn St Savannah GA 31419 USA;

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原文格式 PDF
正文语种 eng
中图分类代数、数论、组合理论;
关键词
Betti numbers; squarefree monomial ideals; domino tiling;

机译：Betti Numbers;SquareFree单体理想;Domino Tiling;

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专利

1. Minimal free resolutions of 2 x n domino tilings [J] . Bouchat Rachelle R., Brown Tricia Muldoon Journal of algebra and its applications . 2019,第6期

机译：最小的自由分辨率为2 x N Domino Tilings
2. On the minimal free resolution of the universal ring for resolutions of length two [J] . Andrew R. Kustin, Jerzy M. Weyman Journal of Algebra . 2007,第2期

机译：关于长度为2的通用环的最小自由分辨率
3. The minimal free resolution of a class of square-free monomial ideals [J] . Zaare-Nahandi R. Journal of pure and applied algebra . 2004,第1a3期

机译：一类无平方单项理想的最小自由分辨率
4. Random Three-Dimensional Tilings of Aztec Octahedra and Tetrahedra: An Extension of Domino Tilings [C] . Dana Randall, Gary Yngve ACM-SIAM Symposium on Discrete Algorithms . 2000

机译：Aztec Octahedra和Tetrahedra的随机三维倾斜：Domino Tilings的延伸
5. A New Approach to Counting Domino Tilings of an m × n Board [D] . Rizer, Williem L. 2020

机译：计算M×N板Domino倾斜的新方法
6. Genome-wide detection of predicted non-coding RNAs in Rhizobium etli expressed during free-living and host-associated growth using a high-resolution tiling array [O] . Maarten Vercruysse, Maarten Fauvart, Lore Cloots, 2010

机译：全基因组范围内使用高分辨率切片阵列检测在自由生活和与宿主相关的生长过程中表达的根瘤菌中预测的非编码RNA
7. Domino tilings and the six-vertex model at its free fermion point [O] . Ferrari, Patrik L., Spohn, Herbert 2006

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Minimal free resolutions of 2 x n domino tilings

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