Article
Mathematics, Applied
Yves Baudelaire Fomatati
Summary: This paper improves the algorithm for matrix factorization of polynomials, obtaining better results by refining the construction of one of the main ingredients of the algorithm.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics
Ming-Zhu Chen, A-Ming Liu, Xiao-Dong Zhang
Summary: In this paper, a sharp upper bound for the spectral radius of an n-vertex F-minor-free graph is presented, and the graphs that achieve this bound are characterized. This result is of significant importance in the field of mathematics.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics
Jozsef Balogh, Ce Chen, Grace Mccourt, Cassie Murley
Summary: This article studies the case of small cliques in the Ramsey-Turan number RT(n, H, f(n)), and proves that these cliques have phase transitions under certain conditions using mathematical methods.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics
Adam Gowty, Daniel Horsley, Adam Mammoliti
Summary: This article determines the minimum value of a family F, denoted as |F-up down arrow|, as a function of the size of the ground set and the family itself. It solves the isoperimetric problem on a graph and provides insights into the isoperimetric problem for hypercubes. Additionally, it has implications for the study of cross-Sperner families.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics
Malgorzata Bednarska-Bzdega
Summary: This article introduces the Ramsey game played on the edge set of K-N and investigates the online Ramsey number. The research finds that when the number of vertices k is less than n and n approaches infinity, the upper bound of the number of rounds in the game is (5/3 + o(1))n. Furthermore, it is proven that when n≥10, the upper bound of the number of rounds in the game is [7n/5] - 1, improving the previous result obtained by J. Cyman, T. Dzido, J. Lapinskas, and A. Lo and verifying their conjecture (r) over tilde (P-4, P-n) = [7n/5] - 1.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics, Applied
Mikhailo Dokuchaev, Itailma Rocha
Summary: In this study, we construct an abelian group C(Theta/R) formed by the isomorphism classes of partial generalized crossed products related to a unital partial representation Theta of a group G into the Picard semigroup PicS(R) of a non-necessarily commutative unital ring R. We identify an appropriate second partial cohomology group of G with a naturally defined subgroup C0(Theta/R) of C(Theta/R). Using these results, we generalize the works by Kanzaki and Miyashita by giving an analogue of the Chase-Harrison-Rosenberg exact sequence associated with an extension of rings and a unital partial representation of an arbitrary group into the monoid of R-subbimodules.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Alexei Entin, Noam Pirani
Summary: This paper proves the existence of a Galois extension with ramification only at infinity for symmetric and alternating groups over finite fields of odd characteristic.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Isaac Moselle
Summary: We demonstrate the homological stability for the family of Iwahori-Hecke algebras of type Bn, where homology is recognized by the relevant Tor group. This family of algebras is linked to the Coxeter groups of type Bn, which are groups of signed permutations. This result extends Hepworth's findings for Iwahori-Hecke algebras of type An.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Dmitri Pavlov
Summary: We prove that categories enriched in the Thomason model structure have a model structure that is Quillen equivalent to the Bergner model structure on simplicial categories, providing a new model for (infinity, 1)-categories. In addition, we construct model structures on modules and monoids in the Thomason model structure and prove that any model structure on the category of small categories that has the same weak equivalences as the Thomason model structure is not a cartesian model structure.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics
Donggyu Kim, Sang-il Oum
Summary: The article explores the essential properties of prime graphs and provides conditions for the existence of non-essential vertices. The research findings are of significant importance for understanding the structure and properties of graphs.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics, Applied
Markus Thuresson
Summary: Hereditary algebras are quasi-hereditary and exhibit certain regularity properties with respect to adapted partial orders. This article investigates the Ext-algebra of standard modules over path algebras of linear quivers and provides necessary and sufficient conditions for regular exact Borel subalgebras. The findings have implications for the understanding of linear quivers with arbitrary orientations.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Edward L. Green, Sibylle Schroll
Summary: This paper studies the ideal C in the path algebra KQ, proving that KQ/C is always finite dimensional with finite global dimension, and it is Morita equivalent to an incidence algebra.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Adeel A. Khan
Summary: This paper constructs a cdh-local motivic homotopy category SHcdh(S) over an arbitrary base scheme S, and shows that there is a canonical equivalence SHcdh(S) similar to or equal to SH(S).
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics
Peter Frankl, Jian Wang
Summary: In this paper, it is proven that for n > 36k, any intersecting family F subset of (((k))([n])) has a diversity of at most ((n-3)(k-2)), improving upon the previous best bound n > 72k.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics
Samantha L. Dahlberg, Hemanshu Kaul, Jeffrey A. Mudrock
Summary: DP-coloring is a generalization of list coloring that calculates the minimum number of DP-colorings in a graph's cover. This paper presents a new approach to compute the DP-coloring number and provides improved bounds compared to existing methods. It also proves that the DP-color function is not chromatic adherent.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics, Applied
Cordian Riener, Robin Schabert
Summary: This article focuses on the geometry of a class of hyperbolic polynomial families determined by linear conditions on the coefficients. These polynomials have all their roots on the real line. The set of hyperbolic polynomials is stratified according to the multiplicities of the real zeros, and this stratification also applies to the hyperbolic slices. The study shows that the local extreme points of hyperbolic slices correspond to hyperbolic polynomials with at most k distinct roots, and that the convex hull of such a family is generally a polyhedron. The article also explores the implications of these results for symmetric real varieties and symmetric semi-algebraic sets, particularly in terms of sparse representations and sampling.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
He-Xia Ni, Li-Yuan Wang
Summary: In this paper, we investigate q-congruences on double basic hypergeometric sums and confirm several conjectures proposed by Zhi-Wei Sun using the 'creative microscoping' method and summation and transformation formulas for basic hypergeometric series.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Bin Qian
Summary: In this paper, a refined Hamilton's gradient estimate for the heat equation is presented, along with new Harnack inequalities and bounds of the associated heat kernels. Inspired by Yau's work, a generalized Li-Yau gradient estimate for the linear heat equation is obtained, extending some known results and generating new gradient estimates.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Dibyajyoti Hazarika, Jayanta Borah, Bhupendra Kumar Singh
Summary: In this article, we investigate the existence and controllability of mild solutions of nonlocal fractional dynamical system with almost sectorial operator. The system involves Caputo fractional derivative of order alpha is an element of (0, 1). The existence results are proved using fixed point theorems with suitable assumptions. Sufficient conditions for controllability are derived using appropriate control function via Leray-Schauder fixed point theorem.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Limin Zhu
Summary: This paper studies the inviscid compressible Cattaneo-Christov system in one-dimensional space. The iterative method is used to establish the local well-posedness of this system for large data in critical Besov spaces based on the L2 framework. Moreover, the global existence of a strong solution can be proved when the initial perturbation around a constant state is sufficiently small, using the renormalized energy method.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
