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Relevant bibliographies by topics / Graded Betti number

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Journal articles

Academic literature on the topic 'Graded Betti number'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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Journal articles on the topic "Graded Betti number"

1

Richert, Benjamin P. "Smallest Graded Betti Numbers." Journal of Algebra 244, no. 1 (2001): 236–59. http://dx.doi.org/10.1006/jabr.2001.8878.

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2

Brun, Morten, та Tim Römer. "Betti Numbers of ℤn-Graded Modules". Communications in Algebra 32, № 12 (2004): 4589–99. http://dx.doi.org/10.1081/agb-200036803.

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3

Bouchat, Rachelle R., and Tricia Muldoon Brown. "Multi-graded Betti numbers of path ideals of trees." Journal of Algebra and Its Applications 16, no. 01 (2017): 1750018. http://dx.doi.org/10.1142/s0219498817500189.

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A path ideal of a tree is an ideal whose minimal generating set corresponds to paths of a specified length in a tree. We provide a description of a collection of induced subtrees whose vertex sets correspond to the multi-graded Betti numbers on the linear strand in the corresponding minimal free resolution of the path ideal. For two classes of path ideals, we give an explicit description of a collection of induced subforests whose vertex sets correspond to the multi-graded Betti numbers in the corresponding minimal free resolutions. Lastly, in both classes of path ideals considered, the graded

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4

Ahmad Rather, Shahnawaz, and Pavinder Singh. "Graded Betti numbers of crown edge ideals." Communications in Algebra 47, no. 4 (2019): 1690–98. http://dx.doi.org/10.1080/00927872.2018.1513018.

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5

Francisco, Christopher A. "Minimal Graded Betti Numbers and Stable Ideals." Communications in Algebra 31, no. 10 (2003): 4971–87. http://dx.doi.org/10.1081/agb-120023142.

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6

Ananthnarayan, H., and Rajiv Kumar. "Extremal rays of Betti cones." Journal of Algebra and Its Applications 19, no. 02 (2019): 2050027. http://dx.doi.org/10.1142/s0219498820500279.

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We study the Betti cone of modules of a standard graded algebra over a field, and find a class of modules whose Betti diagrams span extremal rays of the Betti cone. We also identify a class of one-dimensional Cohen–Macaulay rings with certain Hilbert series, for which the Betti cone is spanned by these extremal rays. These results lead to an algorithm for the decomposition of Betti table of modules, into the extremal rays, over such rings, and also help to obtain bounds for the multiplicity of the given module.

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7

Llamas, Aurora, and Josá Martínez–Bernal. "Cover Product and Betti Polynomial of Graphs." Canadian Mathematical Bulletin 58, no. 2 (2015): 320–33. http://dx.doi.org/10.4153/cmb-2015-013-3.

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AbstractThe cover product of disjoint graphs G and H with fixed vertex covers C(G) and C(H), is the graphwith vertex set V(G) ∪ V(H) and edge setWe describe the graded Betti numbers of GeH in terms of those of. As applications we obtain: (i) For any positive integer k there exists a connected bipartite graph G such that reg R/I(G) = μS(G) + k, where, I(G) denotes the edge ideal of G, reg R/I(G) is the Castelnuovo–Mumford regularity of R/I(G) and μS(G) is the induced or strong matching number of G; (ii)The graded Betti numbers of the complement of a tree depends only upon its number of vertices

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8

Marco-Buzunáriz, M. A., and J. Martín-Morales. "Graded Betti Numbers of the Logarithmic Derivation Module." Communications in Algebra 38, no. 11 (2010): 4348–61. http://dx.doi.org/10.1080/00927870903366918.

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9

Failla, Gioia, and Zhongming Tang. "On the Betti polynomials of certain graded ideals." Communications in Algebra 46, no. 7 (2017): 3135–46. http://dx.doi.org/10.1080/00927872.2017.1404077.

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10

Herzog, Jürgen, Volkmar Welker, and Siamak Yassemi. "Homology of Powers of Ideals: Artin-Rees Numbers of Syzygies and the Golod Property." Algebra Colloquium 23, no. 04 (2016): 689–700. http://dx.doi.org/10.1142/s1005386716000584.

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Let R0 be a Noetherian local ring and R a standard graded R0-algebra with maximal ideal 𝔪 and residue class field 𝕂 = R/𝔪. For a graded ideal I in R we show that for k ≫ 0: (1) the Artin-Rees number of the syzygy modules of Ik as submodules of the free modules from a free resolution is constant, and thereby the Artin-Rees number can be presented as a proper replacement of regularity in the local situation; and (2) R is a polynomial ring over the regular R0, the ring R/Ik is Golod, its Poincaré-Betti series is rational and the Betti numbers of the free resolution of 𝕂 over R/Ik are polynomials

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