Discret. Math. Theor. Comput. Sci.最新文献

Series acceleration formulas obtained from experimentally discovered hypergeometric recursions 由实验发现的超几何递归得到的级数加速度公式

Discret. Math. Theor. Comput. Sci. Pub Date : 2022-12-20 DOI: 10.46298/dmtcs.9557

P. Levrie, J. Campbell

引用次数: 2

Distinct Angles and Angle Chains in Three Dimensions 三维中的不同角度和角链

Discret. Math. Theor. Comput. Sci. Pub Date : 2022-08-28 DOI: 10.46298/dmtcs.10037

R. Ascoli, Livia Betti, J. L. Duke, Xuyan Liu, Wyatt Milgrim, Steven J. Miller, E. Palsson, F. Acosta, Santiago Velazquez Iannuzzelli

{"title":"Distinct Angles and Angle Chains in Three Dimensions","authors":"R. Ascoli, Livia Betti, J. L. Duke, Xuyan Liu, Wyatt Milgrim, Steven J. Miller, E. Palsson, F. Acosta, Santiago Velazquez Iannuzzelli","doi":"10.46298/dmtcs.10037","DOIUrl":"https://doi.org/10.46298/dmtcs.10037","url":null,"abstract":"In 1946, ErdH{o}s posed the distinct distance problem, which seeks to find\u0000the minimum number of distinct distances between pairs of points selected from\u0000any configuration of $n$ points in the plane. The problem has since been\u0000explored along with many variants, including ones that extend it into higher\u0000dimensions. Less studied but no less intriguing is ErdH{o}s' distinct angle\u0000problem, which seeks to find point configurations in the plane that minimize\u0000the number of distinct angles. In their recent paper \"Distinct Angles in\u0000General Position,\" Fleischmann, Konyagin, Miller, Palsson, Pesikoff, and Wolf\u0000use a logarithmic spiral to establish an upper bound of $O(n^2)$ on the minimum\u0000number of distinct angles in the plane in general position, which prohibits\u0000three points on any line or four on any circle.\u0000 We consider the question of distinct angles in three dimensions and provide\u0000bounds on the minimum number of distinct angles in general position in this\u0000setting. We focus on pinned variants of the question, and we examine explicit\u0000constructions of point configurations in $mathbb{R}^3$ which use\u0000self-similarity to minimize the number of distinct angles. Furthermore, we\u0000study a variant of the distinct angles question regarding distinct angle chains\u0000and provide bounds on the minimum number of distinct chains in $mathbb{R}^2$\u0000and $mathbb{R}^3$.","PeriodicalId":110830,"journal":{"name":"Discret. Math. Theor. Comput. Sci.","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116507187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

A heuristic technique for decomposing multisets of non-negative integers according to the Minkowski sum 根据闵可夫斯基和分解非负整数多集的一种启发式技术

Discret. Math. Theor. Comput. Sci. Pub Date : 2022-07-31 DOI: 10.46298/dmtcs.9877

L. Margara

{"title":"A heuristic technique for decomposing multisets of non-negative integers according to the Minkowski sum","authors":"L. Margara","doi":"10.46298/dmtcs.9877","DOIUrl":"https://doi.org/10.46298/dmtcs.9877","url":null,"abstract":"We study the following problem. Given a multiset $M$ of non-negative\u0000integers, decide whether there exist and, in the positive case, compute two\u0000non-trivial multisets whose Minkowski sum is equal to $M$. The Minkowski sum of\u0000two multisets A and B is a multiset containing all possible sums of any element\u0000of A and any element of B. This problem was proved to be NP-complete when\u0000multisets are replaced by sets. This version of the problem is strictly related\u0000to the factorization of boolean polynomials that turns out to be NP-complete as\u0000well. When multisets are considered, the problem is equivalent to the\u0000factorization of polynomials with non-negative integer coefficients. The\u0000computational complexity of both these problems is still unknown.\u0000 The main contribution of this paper is a heuristic technique for decomposing\u0000multisets of non-negative integers. Experimental results show that our\u0000heuristic decomposes multisets of hundreds of elements within seconds\u0000independently of the magnitude of numbers belonging to the multisets. Our\u0000heuristic can be used also for factoring polynomials in N[x]. We show that,\u0000when the degree of the polynomials gets larger, our technique is much faster\u0000than the state-of-the-art algorithms implemented in commercial software like\u0000Mathematica and MatLab.","PeriodicalId":110830,"journal":{"name":"Discret. Math. Theor. Comput. Sci.","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121414536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The 2-colouring problem for (m,n)-mixed graphs with switching is polynomial 具有切换的(m,n)混合图的二次着色问题是一个多项式问题

Discret. Math. Theor. Comput. Sci. Pub Date : 2022-03-15 DOI: 10.46298/dmtcs.9242

R. Brewster, A. Kidner, G. MacGillivray

引用次数: 1

Further enumeration results concerning a recent equivalence of restricted inversion sequences 关于限制反转序列最近等价的进一步枚举结果

Discret. Math. Theor. Comput. Sci. Pub Date : 2022-02-07 DOI: 10.46298/dmtcs.8330

T. Mansour, M. Shattuck

{"title":"Further enumeration results concerning a recent equivalence of restricted inversion sequences","authors":"T. Mansour, M. Shattuck","doi":"10.46298/dmtcs.8330","DOIUrl":"https://doi.org/10.46298/dmtcs.8330","url":null,"abstract":"Let asc and desc denote respectively the statistics recording the number of ascents or descents in a sequence having non-negative integer entries. In a recent paper by Andrews and Chern, it was shown that the distribution of asc on the inversion sequence avoidance class $I_n(geq,neq,>)$ is the same as that of $n-1-text{asc}$ on the class $I_n(>,neq,geq)$, which confirmed an earlier conjecture of Lin. In this paper, we consider some further enumerative aspects related to this equivalence and, as a consequence, provide an alternative proof of the conjecture. In particular, we find recurrence relations for the joint distribution on $I_n(geq,neq,>)$ of asc and desc along with two other parameters, and do the same for $n-1-text{asc}$ and desc on $I_n(>,neq,geq)$. By employing a functional equation approach together with the kernel method, we are able to compute explicitly the generating function for both of the aforementioned joint distributions, which extends (and provides a new proof of) the recent result $|I_n(geq,neq,>)|=|I_n(>,neq,geq)|$. In both cases, an algorithm is formulated for computing the generating function of the asc distribution on members of each respective class having a fixed number of descents.","PeriodicalId":110830,"journal":{"name":"Discret. Math. Theor. Comput. Sci.","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128864679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

Proximity, remoteness and maximum degree in graphs 图中的接近度、距离和最大度

Discret. Math. Theor. Comput. Sci. Pub Date : 2022-01-23 DOI: 10.46298/dmtcs.9432

P. Dankelmann, Sonwabile Mafunda, Sufiyan Mallu

引用次数: 1

Improved product structure for graphs on surfaces 改进了曲面上图形的乘积结构

Discret. Math. Theor. Comput. Sci. Pub Date : 2021-12-18 DOI: 10.46298/dmtcs.8877

Marc Distel, Robert Hickingbotham, T. Huynh, D. Wood

引用次数: 15

Induced betweenness in order-theoretic trees 序理论树的诱导间性

Discret. Math. Theor. Comput. Sci. Pub Date : 2021-11-30 DOI: 10.46298/dmtcs.7288

B. Courcelle

{"title":"Induced betweenness in order-theoretic trees","authors":"B. Courcelle","doi":"10.46298/dmtcs.7288","DOIUrl":"https://doi.org/10.46298/dmtcs.7288","url":null,"abstract":"The ternary relation B(x,y,z) of betweenness states that an element y is between the elements x and z, in some sense depending on the considered structure. In a partially ordered set (N,≤), B(x,y,z):⇔x<y<z∨z<y<x, and the corresponding betweenness structure is (N,B). The class of betweenness structures of linear orders is first-order definable. That of partial orders is monadic second-order definable. An order-theoretic tree is a partial order such that the set of elements larger that any element is linearly ordered and any two elements have an upper-bound. Finite or infinite rooted trees ordered by the ancestor relation are order-theoretic trees. In an order-theoretic tree, B(x,y,z) means that x<y<z or z<y<x or x<y≤x⊔z or z<y≤x⊔z, where x⊔z is the least upper-bound of incomparable elements x and z. In a previous article, we established that the corresponding class of betweenness structures is monadic second-order definable.We prove here that the induced substructures of the betweenness structures of the countable order-theoretic trees form a monadic second-order definable class, denoted by IBO. The proof uses a variant of cographs, the partitioned probe cographs, and their known six finite minimal excluded induced subgraphs called the bounds of the class. This proof links two apparently unrelated topics: cographs and order-theoretic trees.However, the class IBO has finitely many bounds, i.e., minimal excluded finite induced substructures. Hence it is first-order definable. The proof of finiteness uses well-quasi-orders and does not provide the finite list of bounds. Hence, the associated first-order defining sentence is not known.","PeriodicalId":110830,"journal":{"name":"Discret. Math. Theor. Comput. Sci.","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116232266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Span of a Graph: Keeping the Safety Distance 图的跨度:保持安全距离

Discret. Math. Theor. Comput. Sci. Pub Date : 2021-11-17 DOI: 10.46298/dmtcs.9859

I. Banič, A. Taranenko

引用次数: 4

Zero-sum partitions of Abelian groups of order $2^n$ 2^n阶阿贝尔群的零和划分

Discret. Math. Theor. Comput. Sci. Pub Date : 2021-11-09 DOI: 10.46298/dmtcs.9914

Sylwia Cichacz-Przenioslo, Karol Suchan

{"title":"Zero-sum partitions of Abelian groups of order $2^n$","authors":"Sylwia Cichacz-Przenioslo, Karol Suchan","doi":"10.46298/dmtcs.9914","DOIUrl":"https://doi.org/10.46298/dmtcs.9914","url":null,"abstract":"The following problem has been known since the 80's. Let $Gamma$ be an\u0000Abelian group of order $m$ (denoted $|Gamma|=m$), and let $t$ and $m_i$, $1\u0000leq i leq t$, be positive integers such that $sum_{i=1}^t m_i=m-1$.\u0000Determine when $Gamma^*=Gammasetminus{0}$, the set of non-zero elements of\u0000$Gamma$, can be partitioned into disjoint subsets $S_i$, $1 leq i leq t$,\u0000such that $|S_i|=m_i$ and $sum_{sin S_i}s=0$ for every $i$, $1 leq i leq\u0000t$. It is easy to check that $m_igeq 2$ (for every $i$, $1 leq i leq t$) and\u0000$|I(Gamma)|neq 1$ are necessary conditions for the existence of such\u0000partitions, where $I(Gamma)$ is the set of involutions of $Gamma$. It was\u0000proved that the condition $m_igeq 2$ is sufficient if and only if\u0000$|I(Gamma)|in{0,3}$. For other groups (i.e., for which $|I(Gamma)|neq 3$\u0000and $|I(Gamma)|>1$), only the case of any group $Gamma$ with\u0000$Gammacong(Z_2)^n$ for some positive integer $n$ has been analyzed completely\u0000so far, and it was shown independently by several authors that $m_igeq 3$ is\u0000sufficient in this case. Moreover, recently Cichacz and Tuza proved that, if\u0000$|Gamma|$ is large enough and $|I(Gamma)|>1$, then $m_igeq 4$ is sufficient.\u0000In this paper we generalize this result for every Abelian group of order $2^n$.\u0000Namely, we show that the condition $m_igeq 3$ is sufficient for $Gamma$ such\u0000that $|I(Gamma)|>1$ and $|Gamma|=2^n$, for every positive integer $n$. We\u0000also present some applications of this result to graph magic- and\u0000anti-magic-type labelings.","PeriodicalId":110830,"journal":{"name":"Discret. Math. Theor. Comput. Sci.","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130463377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1