Regularity of powers of (parity) binomial edge ideals

被引：2

作者：

Shen, Yi-Huang ^{[1
]}

Zhu, Guangjun ^{[2
]}

机构：

[1] Univ Sci & Technol China, Sch Math Sci, CAS Wu Wen Tsun Key Lab Math, Hefei 230026, Anhui, Peoples R China

[2] Soochow Univ, Sch Math Sci, Suzhou 215006, Jiangsu, Peoples R China

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2023年 / 57卷 / 01期

关键词：

Regularity; Binomial edge ideal; Parity binomial edge ideal; d-sequences; Almost complete intersection; COHEN-MACAULAY; ORTHOGONAL REPRESENTATIONS; ASYMPTOTIC-BEHAVIOR; SEQUENCES;

D O I：

10.1007/s10801-022-01163-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we provide exact formulas for the regularity of powers of an almost complete intersection ideal I which is generated by a homogeneous d-sequence. As applications, when I is an almost complete intersection, taking the form of a (parity) binomial edge ideal of a connected graph, we can describe explicitly reg(I-t) for t >= 2. The only exception is when I is the parity binomial edge ideal of a graph which is obtained by adding an edge between two disjoint odd cycles.

引用

页码：75 / 100

页数：26

共 37 条

[1] Banerjee A., 2019, Adv. Algebra, V277, P17, DOI [10.1007/978-3-030-11521-02, DOI 10.1007/978-3-030-11521-02, 10.1007/978-3-030-11521-0\\_2]
[2] Berlekamp D, 2012, MATH RES LETT, V19, P109
[3] Regularity of powers of forests and cycles
Beyarslan, Selvi
Ha, Huy Tai
Tran Nam Trung
[J]. JOURNAL OF ALGEBRAIC COMBINATORICS, 2015, 42 (04) : 1077 - 1095
[4] Binomial edge ideals of bipartite graphs
Bolognini, Davide
Macchia, Antonio
Strazzanti, Francesco
[J]. EUROPEAN JOURNAL OF COMBINATORICS, 2018, 70 : 1 - 25
[5] Asymptotic behaviour of the Castelnuovo-Mumford regularity
Cutkosky, SD
Herzog, J
Trung, NV
[J]. COMPOSITIO MATHEMATICA, 1999, 118 (03) : 243 - 261
[6] NOTES ON REGULARITY STABILIZATION
Eisenbud, David
Ulrich, Bernd
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 140 (04) : 1221 - 1232
[7] POWERS OF BINOMIAL EDGE IDEALS WITH QUADRATIC GRoBNER BASES
Ene, Viviana
Rinaldo, Giancarlo
Terai, Naoki
[J]. NAGOYA MATHEMATICAL JOURNAL, 2022, 246 : 233 - 255
[8] On the regularity of binomial edge ideals
Ene, Viviana
Zarojanu, Andrei
[J]. MATHEMATISCHE NACHRICHTEN, 2015, 288 (01) : 19 - 24
[9] COHEN-MACAULAY BINOMIAL EDGE IDEALS
Ene, Viviana
Herzog, Juergen
Hibi, Takayuki
[J]. NAGOYA MATHEMATICAL JOURNAL, 2011, 204 : 57 - 68
[10] Grayson D., MACAULAY2 SOFTWARE S

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