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Projective hypersurfaces in tropical scheme theory I: the Macaulay ideal. [PDF]

open access: yesRes Math Sci
Fink A   +3 more
europepmc   +1 more source

Integration of Gestalt Therapy with Evidence-Based Interventions for Borderline Personality Disorder-Theoretical Framework and Clinical Model. [PDF]

open access: yesBrain Sci
Moretto E   +8 more
europepmc   +1 more source

Bounding Projective Dimension [PDF]

open access: yes, 2013
This paper is a survey of progress on Stillman’s Question: Let J be a homogeneous ideal in a standard graded polynomial ring over a field. Is there a bound on the projective dimension of J depending only on the number of elements in a minimal system of homogenoeus generators of J and their degrees (in particular, independent of the number of variables)?
J. McCullough, A. Seceleanu
semanticscholar   +2 more sources
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On Regularity and Projective Dimension of Invariant Chains of Monomial Ideals

The Michigan mathematical journal, 2022
Ideals in infinite-dimensional polynomial rings that are invariant under the action of the monoid of increasing functions have been extensively studied recently.
D. Le, H. D. Nguyen
semanticscholar   +1 more source

Morse resolutions of powers of square-free monomial ideals of projective dimension one

Journal of Algebraic Combinatorics, 2021
Let I be a square-free monomial ideal of projective dimension one. Starting with the Taylor complex on the generators of Ir\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage ...
Susan M. Cooper   +6 more
semanticscholar   +1 more source

Affine semigroups of maximal projective dimension

Collectanea Mathematica, 2021
A submonoid of $$ {\mathbb {N}}^d $$ N d is of maximal projective dimension ( $${\text {MPD}}$$ MPD ) if the associated affine semigroup ring has the maximum possible projective dimension.
O. Bhardwaj, Kriti Goel, I. Sengupta
semanticscholar   +1 more source

Projective Dimension of Some Graphs

Creative Mathematics and Informatics, 2022
In this paper exact values for the projective dimension of edge ideals associated to some star related graphs and product graphs $G\ \square\ P_2$, when $G=\ C_n,\ K_n$ and upper bounds for the projective dimension when $G=\ P_n,\ W_n$, are obtained. We have proved that $pd(C_{n+1}\ \square\ P_2)= 2\big(n-\left\lfloor \frac{n}{4}\right\rfloor\big)
Thankachan, Reji   +2 more
openaire   +2 more sources

Projective Dimension and Regularity of Powers of Edge Ideals of Vertex-Weighted Rooted Forests

Bulletin of the Malaysian Mathematical Sciences Society, 2019
In this paper, we provide some exact formulas for the projective dimension and regularity of powers of edge ideals of some vertex-weighted rooted forests. These formulas are functions of the weight of vertices and the number of edges.
Li Xu, G. Zhu, Hong Wang, Jiaqi Zhang
semanticscholar   +1 more source

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