Discrete Mathematics最新文献_第10页

On the oriented diameter of near planar triangulations

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-01-23 DOI: 10.1016/j.disc.2025.114406

Yiwei Ge , Xiaonan Liu , Zhiyu Wang

引用次数: 0

Three classes of propagation rules for generalized Reed-Solomon codes and their applications to EAQECCs

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-01-22 DOI: 10.1016/j.disc.2025.114405

Ruhao Wan, Shixin Zhu

{"title":"Three classes of propagation rules for generalized Reed-Solomon codes and their applications to EAQECCs","authors":"Ruhao Wan, Shixin Zhu","doi":"10.1016/j.disc.2025.114405","DOIUrl":"10.1016/j.disc.2025.114405","url":null,"abstract":"<div><div>In this paper, we study the Hermitian hulls of generalized Reed-Solomon (GRS) codes over finite fields. For a given class of GRS codes, by extending the length, increasing the dimension, and extending the length and increasing the dimension at the same time, we obtain three classes of GRS codes with Hermitian hulls of arbitrary dimensions. Furthermore, based on some known <span><math><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-ary Hermitian self-orthogonal GRS codes with dimension <span><math><mi>q</mi><mo>−</mo><mn>1</mn></math></span>, we obtain several classes of <span><math><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-ary maximum distance separable (MDS) codes with Hermitian hulls of arbitrary dimensions. It is worth noting that the dimension of these MDS codes can be taken from <em>q</em> to <span><math><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>, and the parameters of these MDS codes can be more flexible by propagation rules. As an application, we derive three new propagation rules for MDS entanglement-assisted quantum error correction codes (EAQECCs) constructed from GRS codes. Then, from the presently known GRS codes with Hermitian hulls, we can directly obtain many MDS EAQECCs with more flexible parameters. Finally, we present several new classes of (MDS) EAQECCs with flexible parameters, and the distance of these codes can be taken from <span><math><mi>q</mi><mo>+</mo><mn>1</mn></math></span> to <span><math><mfrac><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 5","pages":"Article 114405"},"PeriodicalIF":0.7,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143290023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Eigenvalues and toughness of regular graphs

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-01-21 DOI: 10.1016/j.disc.2025.114404

Yuanyuan Chen , Huiqiu Lin , Zhiwen Wang

引用次数: 0

A generalization of the Tang-Ding binary cyclic codes

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-01-21 DOI: 10.1016/j.disc.2024.114390

Ling Li , Minjia Shi , Sihui Tao , Zhonghua Sun , Shixin Zhu , Jon-Lark Kim , Patrick Solé

{"title":"A generalization of the Tang-Ding binary cyclic codes","authors":"Ling Li , Minjia Shi , Sihui Tao , Zhonghua Sun , Shixin Zhu , Jon-Lark Kim , Patrick Solé","doi":"10.1016/j.disc.2024.114390","DOIUrl":"10.1016/j.disc.2024.114390","url":null,"abstract":"<div><div>Cyclic codes are an interesting family of linear codes since they have efficient decoding algorithms and contain optimal codes as subfamilies. Constructing infinite families of cyclic codes with good parameters is important in both theory and practice. Recently, Tang and Ding (2022) <span><span>[34]</span></span> proposed an infinite family of binary cyclic codes with good parameters. Shi et al. [<span><span>arXiv:2309.12003v1</span><svg><path></path></svg></span>, 2023] extended the binary Tang-Ding codes to the 4-ary case. Inspired by these two works, we study <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>s</mi></mrow></msup></math></span>-ary Tang-Ding codes, where <span><math><mi>s</mi><mo>≥</mo><mn>2</mn></math></span>. Good lower bounds on the minimum distance of the <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>s</mi></mrow></msup></math></span>-ary Tang-Ding codes are presented. As a by-product, an infinite family of <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>s</mi></mrow></msup></math></span>-ary duadic codes with a square-root like lower bound is presented.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 5","pages":"Article 114390"},"PeriodicalIF":0.7,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143290024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Modulus for bases of matroids

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-01-16 DOI: 10.1016/j.disc.2025.114395

Huy Truong, Pietro Poggi-Corradini

引用次数: 0

On a family of automatic apwenian sequences

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-01-16 DOI: 10.1016/j.disc.2025.114399

Ying-Jun Guo , Guo-Niu Han

{"title":"On a family of automatic apwenian sequences","authors":"Ying-Jun Guo , Guo-Niu Han","doi":"10.1016/j.disc.2025.114399","DOIUrl":"10.1016/j.disc.2025.114399","url":null,"abstract":"<div><div>An integer sequence <span><math><msub><mrow><mo>{</mo><mi>a</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>}</mo></mrow><mrow><mi>n</mi><mo>≥</mo><mn>0</mn></mrow></msub></math></span> is called <em>apwenian</em> if <span><math><mi>a</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>1</mn></math></span> and <span><math><mi>a</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>≡</mo><mi>a</mi><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>+</mo><mi>a</mi><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo><mspace></mspace><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>2</mn><mo>)</mo></math></span> for all <span><math><mi>n</mi><mo>≥</mo><mn>0</mn></math></span>. The apwenian sequences are connected with the Hankel determinants, the continued fractions, the rational approximations and the measures of randomness for binary sequences. In this paper, we study the automatic apwenian sequences over different alphabets. On the alphabet <span><math><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></span>, we give an extension of the generalized Rueppel sequences and characterize all the 2-automatic apwenian sequences in this class. On the alphabet <span><math><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></math></span>, we prove that the only apwenian sequence, among all fixed points of substitutions of constant length, is the period-doubling like sequence. On the other alphabets, we give a description of the 2-automatic apwenian sequences in terms of 2-uniform morphisms. Moreover, we find two 3-automatic apwenian sequences on the alphabet <span><math><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></math></span>.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 5","pages":"Article 114399"},"PeriodicalIF":0.7,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143289907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Asymptotics of self-overlapping permutations

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-01-16 DOI: 10.1016/j.disc.2025.114400

Sergey Kirgizov , Khaydar Nurligareev

引用次数: 0

Domination and packing in graphs

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-01-15 DOI: 10.1016/j.disc.2025.114393

Renzo Gómez , Juan Gutiérrez

{"title":"Domination and packing in graphs","authors":"Renzo Gómez , Juan Gutiérrez","doi":"10.1016/j.disc.2025.114393","DOIUrl":"10.1016/j.disc.2025.114393","url":null,"abstract":"<div><div>Given a graph <em>G</em>, the domination number <span><math><mi>γ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is the minimum cardinality of a dominating set in <em>G</em>, and the packing number <span><math><mi>ρ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is the minimum cardinality of a set of vertices whose pairwise distance is at least three. The inequality <span><math><mi>ρ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≤</mo><mi>γ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is well-known. Furthermore, Henning et al. conjectured that <span><math><mi>γ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≤</mo><mn>2</mn><mi>ρ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>+</mo><mn>1</mn></math></span> if <em>G</em> is subcubic. In this paper, we show that <span><math><mi>γ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≤</mo><mfrac><mrow><mn>120</mn></mrow><mrow><mn>49</mn></mrow></mfrac><mi>ρ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> if <em>G</em> is a bipartite cubic graph. This result is obtained by showing that <span><math><mi>ρ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≥</mo><mfrac><mrow><mn>7</mn></mrow><mrow><mn>48</mn></mrow></mfrac><mo>|</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo></math></span> for this class of graphs, which improves a previous bound given by Favaron. We also show that <span><math><mi>γ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≤</mo><mn>3</mn><mi>ρ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> if <em>G</em> is a maximal outerplanar graph, and that <span><math><mi>γ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≤</mo><mn>2</mn><mi>ρ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> if <em>G</em> is a biconvex graph, where the latter result is tight.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 5","pages":"Article 114393"},"PeriodicalIF":0.7,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143221699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Formal self-duality and numerical self-duality for symmetric association schemes

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-01-14 DOI: 10.1016/j.disc.2025.114394

Kazumasa Nomura , Paul Terwilliger

引用次数: 0

Components of domino tilings under flips in quadriculated tori

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-01-14 DOI: 10.1016/j.disc.2025.114396

Qianqian Liu , Yaxian Zhang , Heping Zhang

{"title":"Components of domino tilings under flips in quadriculated tori","authors":"Qianqian Liu , Yaxian Zhang , Heping Zhang","doi":"10.1016/j.disc.2025.114396","DOIUrl":"10.1016/j.disc.2025.114396","url":null,"abstract":"<div><div>In a region <em>R</em> consisting of unit squares, a (domino) tiling is a collection of dominoes (the union of two adjacent squares) which pave fully the region. The flip graph of <em>R</em> is defined on the set of all tilings of <em>R</em> where two tilings are adjacent if we change one from the other by a flip (a <span><math><msup><mrow><mn>90</mn></mrow><mrow><mo>∘</mo></mrow></msup></math></span> rotation of a pair of side-by-side dominoes). If <em>R</em> is simply-connected, then its flip graph is connected. By using homology and cohomology, Saldanha, Tomei, Casarin and Romualdo obtained a criterion to decide if two tilings are in the same component of flip graph of quadriculated surface. By a graph-theoretic method, we obtain that the flip graph of a non-bipartite quadriculated torus consists of two isomorphic components. As an application, we obtain that the forcing numbers of all perfect matchings of each non-bipartite quadriculated torus form an integer-interval. For a bipartite quadriculated torus, the components of the flip graph is more complicated, and we use homology to obtain a general lower bound for the number of components of its flip graph.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 5","pages":"Article 114396"},"PeriodicalIF":0.7,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143352435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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