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Projective hypersurfaces in tropical scheme theory I: the Macaulay ideal. [PDF]
Fink A +3 more
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Integration of Gestalt Therapy with Evidence-Based Interventions for Borderline Personality Disorder-Theoretical Framework and Clinical Model. [PDF]
Moretto E +8 more
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Bounding Projective Dimension [PDF]
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
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On Regularity and Projective Dimension of Invariant Chains of Monomial Ideals
The Michigan mathematical journal, 2022Ideals 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
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Morse resolutions of powers of square-free monomial ideals of projective dimension one
Journal of Algebraic Combinatorics, 2021Let 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
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Affine semigroups of maximal projective dimension
Collectanea Mathematica, 2021A 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
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Projective Dimension of Some Graphs
Creative Mathematics and Informatics, 2022In 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
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Projective Dimension and Regularity of Powers of Edge Ideals of Vertex-Weighted Rooted Forests
Bulletin of the Malaysian Mathematical Sciences Society, 2019In 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
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