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Lattice Cohomology of Partially Ordered Sets 部分有序集合的格同调
IF 0.4 4区 数学
Studia Scientiarum Mathematicarum Hungarica Pub Date : 2024-07-24 DOI: 10.1556/012.2024.04312
Tamás Ágoston, András Némethi
{"title":"Lattice Cohomology of Partially Ordered Sets","authors":"Tamás Ágoston, András Némethi","doi":"10.1556/012.2024.04312","DOIUrl":"https://doi.org/10.1556/012.2024.04312","url":null,"abstract":"In this paper we introduce a construction for a weighted CW complex (and the associated lattice cohomology) corresponding to partially ordered sets with some additional structure. This is a generalization of the construction seen in [4] where we started from a system of subspaces of a given vector space. We then proceed to prove some basic properties of this construction that are in many ways analogous to those seen in the case of subspaces, but some aspects of the construction result in complexities not present in that scenario.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141806541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Planar Turán Number of the Θ6 Θ6的平面图兰数
IF 0.4 4区 数学
Studia Scientiarum Mathematicarum Hungarica Pub Date : 2024-07-24 DOI: 10.1556/012.2024.04307
Chuanqi Xiao, Debarun Ghosh, E. Győri, Addisu Paulos, Oscar Zamora
{"title":"Planar Turán Number of the Θ6","authors":"Chuanqi Xiao, Debarun Ghosh, E. Győri, Addisu Paulos, Oscar Zamora","doi":"10.1556/012.2024.04307","DOIUrl":"https://doi.org/10.1556/012.2024.04307","url":null,"abstract":"Let F be a nonempty family of graphs. A graph 𝐺 is called F -free if it contains no graph from F as a subgraph. For a positive integer 𝑛, the planar Turán number of F, denoted by exp (𝑛, F), is the maximum number of edges in an 𝑛-vertex F -free planar graph.Let Θ𝑘 be the family of Theta graphs on 𝑘 ≥ 4 vertices, that is, graphs obtained by joining a pair of non-consecutive of a 𝑘-cycle with an edge. Lan, Shi and Song determined an upper bound exp (𝑛, Θ6) ≤ 18𝑛/7−36𝑛/7, but for large 𝑛, they did not verify that the bound is sharp. In this paper, we improve their bound by proving exp (𝑛, Θ6) ≤ 18𝑛/−48𝑛/7 and then we demonstrate the existence of infinitely many positive integer 𝑛 and an 𝑛-vertex Θ6-free planar graph attaining the bound.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141808913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Parallel Covering an Obtuse Triangle with Squares 用正方形平行覆盖钝角三角形
IF 0.4 4区 数学
Studia Scientiarum Mathematicarum Hungarica Pub Date : 2024-07-22 DOI: 10.1556/012.2024.04313
Zhanjun Su, Yufang Wu
{"title":"Parallel Covering an Obtuse Triangle with Squares","authors":"Zhanjun Su, Yufang Wu","doi":"10.1556/012.2024.04313","DOIUrl":"https://doi.org/10.1556/012.2024.04313","url":null,"abstract":"Suppose that 𝑇 (𝛼, 𝛽) is an obtuse triangle with base length 1 and with base angles 𝛼 and 𝛽 (where 𝛽 > 90◦). In this note a tight lower bound of the sum of the areas of squares that can parallel cover 𝑇 (𝛼, 𝛽) is given. This result complements the previous lower bound obtained for the triangles with the interior angles at the base of the measure not greater than 90◦.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141816561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spanning Trees Whose Stems are Caterpillars 茎是毛毛虫的参天大树
IF 0.4 4区 数学
Studia Scientiarum Mathematicarum Hungarica Pub Date : 2024-07-16 DOI: 10.1556/012.2024.04310
P. Ha, D. Hanh, Le Dinh Nam, Nguyen Huu Nhan
{"title":"Spanning Trees Whose Stems are Caterpillars","authors":"P. Ha, D. Hanh, Le Dinh Nam, Nguyen Huu Nhan","doi":"10.1556/012.2024.04310","DOIUrl":"https://doi.org/10.1556/012.2024.04310","url":null,"abstract":"Let 𝑇 be a tree, a vertex of degree one is called a leaf. The set of all leaves of 𝑇 is denoted by Leaf(𝑇). The subtree 𝑇 − Leaf(𝑇) of 𝑇 is called the stem of 𝑇 and denoted by Stem(𝑇). A tree 𝑇 is called a caterpillar if Stem(𝑇) is a path. In this paper, we give two sufficient conditions for a connected graph to have a spanning tree whose stem is a caterpillar. We also give some examples to show that these conditions are sharp.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141642242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Combinatorial Construction of Bi-Cyclic 4-Polytopes 双环 4-多聚物的组合构造
IF 0.7 4区 数学
Studia Scientiarum Mathematicarum Hungarica Pub Date : 2024-04-15 DOI: 10.1556/012.2024.04305
T. Bisztriczky
{"title":"A Combinatorial Construction of Bi-Cyclic 4-Polytopes","authors":"T. Bisztriczky","doi":"10.1556/012.2024.04305","DOIUrl":"https://doi.org/10.1556/012.2024.04305","url":null,"abstract":"A bi-cyclic 4-polytope in ℝ4 was introduced by Z. Smilansky as the convex hull of evenly spaced points on a generalized trigonometric moment curve in ℝ4. We present combinatorial geometric conditions that yield the face lattices of a class of such 4-polytopes.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140702969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Results on Extremal Graph Theoretic Questions for Q-Ary Vectors Q-Ary 向量的极值图论问题研究成果
IF 0.7 4区 数学
Studia Scientiarum Mathematicarum Hungarica Pub Date : 2024-03-28 DOI: 10.1556/012.2023.04303
Koppány Encz, Márton Marits, Benedek Váli, Máté Weisz
{"title":"Results on Extremal Graph Theoretic Questions for Q-Ary Vectors","authors":"Koppány Encz, Márton Marits, Benedek Váli, Máté Weisz","doi":"10.1556/012.2023.04303","DOIUrl":"https://doi.org/10.1556/012.2023.04303","url":null,"abstract":"A 𝑞-graph with 𝑒 edges and 𝑛 vertices is defined as an 𝑒 × 𝑛 matrix with entries from {0, … , 𝑞}, such that each row of the matrix (called a 𝑞-edge) contains exactly two nonzero entries. If 𝐻 is a 𝑞-graph, then 𝐻 is said to contain an 𝑠-copy of the ordinary graph 𝐹, if a set 𝑆 of 𝑞-edges can be selected from 𝐻 such that their intersection graph is isomorphic to 𝐹, and for any vertex 𝑣 of 𝑆 and any two incident edges 𝑒, 𝑓 ∈ 𝑆 the sum of the entries of 𝑒 and 𝑓 is at least 𝑠. The extremal number ex(𝑛, 𝐹, 𝑞, 𝑠) is defined as the maximal number of edges in an 𝑛-vertex 𝑞-graph such that it does not contain contain an 𝑠-copy of the forbidden graph 𝐹.In the present paper, we reduce the problem of finding ex(𝑛, 𝐹, 𝑞, 𝑞 + 1) for even 𝑞 to the case 𝑞 = 2, and determine the asymptotics of ex(𝑛, 𝐶2𝑘+1, 𝑞, 𝑞 + 1).","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140370024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Maximizing the Area of Polygons via Quasicyclic Polygons 通过准环多边形最大化多边形的面积
IF 0.7 4区 数学
Studia Scientiarum Mathematicarum Hungarica Pub Date : 2024-03-27 DOI: 10.1556/012.2023.04304
Giuseppina Anatriello, Giovanni Vincenzi
{"title":"Maximizing the Area of Polygons via Quasicyclic Polygons","authors":"Giuseppina Anatriello, Giovanni Vincenzi","doi":"10.1556/012.2023.04304","DOIUrl":"https://doi.org/10.1556/012.2023.04304","url":null,"abstract":"Based on Peter’s work from 2003, quadrilaterals can be characterized in the following way: “among all quadrilaterals with given side lengths 𝑎, 𝑏, 𝑐 and 𝑑, those of the largest possible area are exactly the cyclic ones”. In this paper, we will give the corresponding characterization for every polygon, by means of quasicyclic polygons properties.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140375411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximations of Singular Surfaces with Standard Cuspidal Edges 具有标准凸边的奇异曲面的近似值
IF 0.7 4区 数学
Studia Scientiarum Mathematicarum Hungarica Pub Date : 2024-03-27 DOI: 10.1556/012.2023.04301
Kentaro Saji, Yoshiki Yamamoto
{"title":"Approximations of Singular Surfaces with Standard Cuspidal Edges","authors":"Kentaro Saji, Yoshiki Yamamoto","doi":"10.1556/012.2023.04301","DOIUrl":"https://doi.org/10.1556/012.2023.04301","url":null,"abstract":"We consider a function from the Euclidean three space whose zero set is the image of the standard cuspidal edge. The composition of a parametrized singular surface in the three space with this function provides an approximation of the surface by the standard cuspidal edge. Taking a look at singularities of this composition, we study various approximations of singular surfaces like the cross cap, the generalized cuspidal edge and the swallowtail by standard cuspidal edges.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140377146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some Bounds for the Regularity of the Edge Ideals and Their Powers in a Certain Class of Graphs 某类图中边理想及其幂的规则性的一些界限
IF 0.7 4区 数学
Studia Scientiarum Mathematicarum Hungarica Pub Date : 2024-01-29 DOI: 10.1556/012.2023.04298
T. Ashitha, Thangaraj Asir, Do Trong Hoang, M. R. Pournaki
{"title":"Some Bounds for the Regularity of the Edge Ideals and Their Powers in a Certain Class of Graphs","authors":"T. Ashitha, Thangaraj Asir, Do Trong Hoang, M. R. Pournaki","doi":"10.1556/012.2023.04298","DOIUrl":"https://doi.org/10.1556/012.2023.04298","url":null,"abstract":"Let 𝑛 ≥ 2 be an integer. The graph is obtained by letting all the elements of {0, … , 𝑛 − 1} to be the vertices and defining distinct vertices 𝑥 and 𝑦 to be adjacent if and only if gcd(𝑥 + 𝑦, 𝑛) ≠ 1. In this paper, we give some bounds for the Castelnuovo–Mumford regularity of the edge ideals and their powers for .","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140489936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unavoidable Crossings in Finite Coverings 有限覆盖中不可避免的交叉
IF 0.7 4区 数学
Studia Scientiarum Mathematicarum Hungarica Pub Date : 2024-01-29 DOI: 10.1556/012.2023.04300
András Bezdek, W. Kuperberg
{"title":"Unavoidable Crossings in Finite Coverings","authors":"András Bezdek, W. Kuperberg","doi":"10.1556/012.2023.04300","DOIUrl":"https://doi.org/10.1556/012.2023.04300","url":null,"abstract":"Motivated by the examples of Heppes and Wegner, we present several other examples of the following kind: a bounded convex region 𝐷 and a convex disk 𝐾 in the plane are described, such that every thinnest covering of 𝐷 with congruent copies of 𝐾 contains crossing pairs.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140489664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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