scholarly journals Strongly Robust Toric Ideals in Codimension 2

2019 ◽  
Vol 10 (1) ◽  
pp. 128-136 ◽  
Author(s):  
Seth Sullivant
Keyword(s):  
Positive Answer ◽  
Homogeneous Ideal ◽  
Toric Ideals ◽  
Grobner Basis ◽  
Toric Ideal ◽  
Generating Set ◽  
Graver Basis ◽  
Minimal Generating Set ◽  
Gale Diagrams ◽  
Universal Gröbner Basis

A homogeneous ideal is robust if its universal Gröbner basis is also a minimal generating set.  For toric ideals, one has the stronger definition: A toric ideal is strongly robust if its Graver basis equals the set of indispensable binomials.  We characterize the codimension 2  strongly robust toric ideals by their Gale diagrams.  This give a positive answer to a question of Petrovic, Thoma, and Vladoiu in the case of codimension 2 toric ideals.

scholarly journals Divisors on graphs, Connected flags, and Syzygies

2013 ◽  
Vol DMTCS Proceedings vol. AS,... (Proceedings) ◽  
Author(s):  
Fatemeh Mohammadi ◽  
Farbod Shokrieh
Keyword(s):  
Gröbner Basis ◽  
Betti Numbers ◽  
Point Of View ◽  
Grobner Basis ◽  
Generating Set ◽  
Term Order ◽  
Syzygy Module ◽  
International Audience ◽  
The Given ◽  
Minimal Generating Set

International audience We study the binomial and monomial ideals arising from linear equivalence of divisors on graphs from the point of view of Gröbner theory. We give an explicit description of a minimal Gröbner basis for each higher syzygy module. In each case the given minimal Gröbner basis is also a minimal generating set. The Betti numbers of $I_G$ and its initial ideal (with respect to a natural term order) coincide and they correspond to the number of ``connected flags'' in $G$. Moreover, the Betti numbers are independent of the characteristic of the base field.

A Characterization of Left Perfect Rings

1995 ◽  
Vol 38 (3) ◽  
pp. 382-384
Author(s):  
Yiqiang Zhou
Keyword(s):  
Positive Answer ◽  
Generating Set ◽  
Perfect Ring ◽  
Minimal Generating Set

AbstractIn this note, we show that a ring R is a left perfect ring if and only if every generating set of each left R-module contains a minimal generating set. This result gives a positive answer to a question on left perfect rings raised by Nashier and Nichols.

scholarly journals On the Grobner Basis of the Toric Ideal for 3 X n- Contingency Tables

2019 ◽  
pp. 1362-1366
Author(s):  
Hussein S. Mohammed Hussein ◽  
Abdulrahman H. Majeed
Keyword(s):  
Gröbner Basis ◽  
Contingency Tables ◽  
Grobner Basis ◽  
Toric Ideal ◽  
Markov Basis ◽  
Universal Gröbner Basis

In this paper, The Grobner basis of the Toric Ideal for - contingency tables related with the Markov basis B introduced by Hussein S. MH, Abdulrahman H. M in 2018 is found. Also, the Grobner basis is a reduced and universal Grobner basis are shown.

scholarly journals The Universal Gröbner Basis of a Binomial Edge Ideal

10.37236/5912 ◽  
2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Mourtadha Badiane ◽  
Isaac Burke ◽  
Emil Sköldberg
Keyword(s):  
Complete Graph ◽  
Gröbner Basis ◽  
Basis Set ◽  
Edge Ideal ◽  
Grobner Basis ◽  
Graver Basis ◽  
Underlying Graph ◽  
Universal Gröbner Basis

We show that the universal Gröbner basis and the Graver basis of a binomial edge ideal coincide. We provide a description for this basis set in terms of certain paths in the underlying graph. We conjecture a similar result for a parity binomial edge ideal and prove this conjecture for the case when the underlying graph is the complete graph.

scholarly journals The Fundamental Group of Balanced Simplicial Complexes and Posets

10.37236/73 ◽  
2009 ◽  
Vol 16 (2) ◽  
Author(s):  
Steven Klee
Keyword(s):  
Fundamental Group ◽  
Upper Bound ◽  
Large Family ◽  
Simplicial Complexes ◽  
Generating Set ◽  
Minimal Generating Set

We establish an upper bound on the cardinality of a minimal generating set for the fundamental group of a large family of connected, balanced simplicial complexes and, more generally, simplicial posets.

The Fuzziness of a Minimal Generating Set of Fedorov Groups

2021 ◽  
Vol 66 (6) ◽  
pp. 913-919
Author(s):  
A. M. Banaru ◽  
V. R. Shiroky ◽  
D. A. Banaru
Keyword(s):  
Generating Set ◽  
Minimal Generating Set

The Number of Generators of a Linear p-Group

1972 ◽  
Vol 24 (5) ◽  
pp. 851-858 ◽  
Author(s):  
I. M. Isaacs
Keyword(s):  
Generating Set ◽  
Nilpotence Class ◽  
Number Of Generators ◽  
Minimal Generating Set

Let G be a finite p-group, having a faithful character χ of degree f. The object of this paper is to bound the number, d(G), of generators in a minimal generating set for G in terms of χ and in particular in terms of f. This problem was raised by D. M. Goldschmidt, and solved by him in the case that G has nilpotence class 2.

scholarly journals Triple-crossing projections, moves on knots and links and their minimal diagrams

2020 ◽  
Vol 29 (04) ◽  
pp. 2050015 ◽  
Author(s):  
Michał Jabłonowski ◽  
Łukasz Trojanowski
Keyword(s):  
Triple Point ◽  
Crossing Number ◽  
Systematic Method ◽  
Generating Set ◽  
New Type ◽  
Knots And Links ◽  
Minimal Generating Set

In this paper, we present a systematic method to generate prime knot and prime link minimal triple-point projections, and then classify all classical prime knots and prime links with triple-crossing number at most four. We also extend the table of known knots and links with triple-crossing number equal to five. By introducing a new type of diagrammatic move, we reduce the number of generating moves on triple-crossing diagrams, and derive a minimal generating set of moves connecting triple-crossing diagrams of the same knot.

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