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Two series which generalize Dirichlet’s lambda and Riemann’s zeta functions at positive integer arguments 在正整数变元上推广Dirichlet lambda和Riemannζ函数的两个级数
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-08-25 DOI: 10.47443/dml.2023.051
Lubomir Markov
{"title":"Two series which generalize Dirichlet’s lambda and Riemann’s zeta functions at positive integer arguments","authors":"Lubomir Markov","doi":"10.47443/dml.2023.051","DOIUrl":"https://doi.org/10.47443/dml.2023.051","url":null,"abstract":"The series (cid:80) ∞ k =0 G N ( k ) (2 k +1) r and (cid:80) ∞ k =1 H N ( k ) k r are considered, where G N ( k ) and H N ( k ) are the Borwein-Chamberland sums appeared in the expansions of integer powers of the arcsine reported in the paper [D. Borwein, M. Chamberland, Int. J. Math. Math. Sci. 2007 (2007) #1981]. For 3 ≤ r ∈ N , representations for these series in terms of zeta values are derived, extending a theorem proved in the paper [J. Ewell, Canad. Math. Bull. 34 (1991) 60–66]. Several corollaries (especially for the case r = 3 ) are obtained, extending some known representations, including Euler’s famous rapidly converging series for ζ (3) . The technique can be applied to the case r = 2 and it yields generalizations of the formulas (cid:80) ∞ k =0 1 (2 k +1","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46912466","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
Chimneys in compositions and bargraphs 烟囱在构图和柱状图
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-08-11 DOI: 10.47443/dml.2023.103
M. Archibald, A. Blecher, A. Knopfmacher, T. Mansour
{"title":"Chimneys in compositions and bargraphs","authors":"M. Archibald, A. Blecher, A. Knopfmacher, T. Mansour","doi":"10.47443/dml.2023.103","DOIUrl":"https://doi.org/10.47443/dml.2023.103","url":null,"abstract":"Motivated by cut points in graph theory, we consider a similar notion in compositions and bargraphs. This is equivalent to counting r -chimneys (a single column extending beyond its immediate neighbours by at least r cells in a bargraph). We establish generating functions for compositions that avoid or count 2 -chimneys. Thereafter, in the case of bargraphs we provide two methods for obtaining these generating functions as well as asymptotic estimates for the more general r -chimneys where r ≥ 1","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42489012","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
A Gallai’s Theorem type result for the edge stability of graphs 图边稳定性的一个Gallai定理型结果
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-08-11 DOI: 10.47443/dml.2023.088
A. Kemnitz, M. Marangio
{"title":"A Gallai’s Theorem type result for the edge stability of graphs","authors":"A. Kemnitz, M. Marangio","doi":"10.47443/dml.2023.088","DOIUrl":"https://doi.org/10.47443/dml.2023.088","url":null,"abstract":"For an arbitrary invariant ρ ( G ) of a graph G the ρ -edge stability number es ρ ( G ) of G is the minimum number of edges of G whose removal results in a graph H ⊆ G with ρ ( H ) (cid:54) = ρ ( G ) . If such an edge set does not exist, then es ρ ( G ) = ∞ . Gallai’s Theorem states that α (cid:48) ( G ) + β (cid:48) ( G ) = n ( G ) for a graph G without isolated vertices, where α (cid:48) ( G ) is the matching number, β (cid:48) ( G ) the edge covering number, and n ( G ) the order of G . We prove a corresponding result for invariants that are based on the edge stability number es ρ ( G )","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49404332","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
Erratum to: A common approach to three open problems in number theory 勘误表：数论中三个开放问题的通用方法
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-08-07 DOI: 10.47443/dml.2023.049e
A. Tyszka
{"title":"Erratum to: A common approach to three open problems in number theory","authors":"A. Tyszka","doi":"10.47443/dml.2023.049e","DOIUrl":"https://doi.org/10.47443/dml.2023.049e","url":null,"abstract":"","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46982086","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
Moments of the one-shuffle no-feedback card guessing game 一次洗牌，无反馈的猜牌游戏的瞬间
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-08-07 DOI: 10.47443/dml.2023.119
Tipaluck Krityakierne, Poohrich Siriputcharoen, T. Thanatipanonda, Chaloemkiat Yapolha
{"title":"Moments of the one-shuffle no-feedback card guessing game","authors":"Tipaluck Krityakierne, Poohrich Siriputcharoen, T. Thanatipanonda, Chaloemkiat Yapolha","doi":"10.47443/dml.2023.119","DOIUrl":"https://doi.org/10.47443/dml.2023.119","url":null,"abstract":"We consider card guessing with no feedback, a variant of the game previously studied by Ciucu in 1998. In this study, we derive an exact, closed-form formula for the asymptotic (in the number of cards, n ) expected number of correct guesses, as well as higher moments, for a one-time riffle shuffle game under the optimal strategy. The problem is tackled using two different approaches: one approach utilizes a fast generating function based on a recurrence relation to obtain numerical moments, while the other is the symbolic approach employing the method of indicators for finding expected counts. The results obtained contribute to the existing literature on card guessing with no feedback.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47915555","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 eccentricity spread of weak-friendship graphs 弱友谊图的古怪传播
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-08-07 DOI: 10.47443/dml.2023.099
Xuanshi Jia, Xiaohong Li, M. Brunetti
{"title":"The eccentricity spread of weak-friendship graphs","authors":"Xuanshi Jia, Xiaohong Li, M. Brunetti","doi":"10.47443/dml.2023.099","DOIUrl":"https://doi.org/10.47443/dml.2023.099","url":null,"abstract":"A weak-friendship graph is a connected induced subgraph of a friendship graph. The unique graphs attaining the first two smallest eccentricity spread in the class of weak-friendship graphs of given order are determined in this paper","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42456363","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
On colorings and orientations of signed graphs 关于有符号图的着色和方向
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-07-07 DOI: 10.47443/dml.2023.080
Daniel C. Slilaty
{"title":"On colorings and orientations of signed graphs","authors":"Daniel C. Slilaty","doi":"10.47443/dml.2023.080","DOIUrl":"https://doi.org/10.47443/dml.2023.080","url":null,"abstract":"A classical theorem independently due to Gallai and Roy states that a graph G has a proper k -coloring if and only if G has an orientation without coherent paths of length k . An analogue of this result for signed graphs is proved in this article.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46493381","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
Optimal t-rubbling on complete graphs and paths 完全图和路径上的最优t-rub
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-07-04 DOI: 10.47443/dml.2023.089
Nándor Sieben
{"title":"Optimal t-rubbling on complete graphs and paths","authors":"Nándor Sieben","doi":"10.47443/dml.2023.089","DOIUrl":"https://doi.org/10.47443/dml.2023.089","url":null,"abstract":"Given a distribution of pebbles on the vertices of a graph, a rubbling move places one pebble at a vertex and removes a pebble each at two not necessarily distinct adjacent vertices. One pebble is the cost of transportation. A vertex is t -reachable if at least t pebbles can be moved to the vertex using rubbling moves. The optimal t -rubbling number of a graph is the minimum number of pebbles in a pebble distribution that makes every vertex t -reachable. The optimal t -rubbling numbers of complete graphs and paths are determined.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47905824","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 first three largest values of the spectral norm of oriented bicyclic graphs 有向双环图的谱范数的前三个最大值
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-07-04 DOI: 10.47443/dml.2023.082
Kun Wei, Jianping Li
{"title":"The first three largest values of the spectral norm of oriented bicyclic graphs","authors":"Kun Wei, Jianping Li","doi":"10.47443/dml.2023.082","DOIUrl":"https://doi.org/10.47443/dml.2023.082","url":null,"abstract":"Let D be a digraph with n vertices and let σ 1 ( D ) , σ 2 ( D ) , . . . , σ n ( D ) be the singular values of the adjacency matrix of D , where σ 1 ( D ) ≥ σ 2 ( D ) ≥ · · · ≥ σ n ( D ) . The spectral norm of D is σ 1 ( D ) . In this paper, we determine the orientations of graphs with the first three largest values of the spectral norm over the family of all orientations of bicyclic graphs with at least 12 vertices.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45376352","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
Extremal bounds on peripherality measures 外围度量的极值界限
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-06-27 DOI: 10.47443/dml.2023.148
L. Tang
{"title":"Extremal bounds on peripherality measures","authors":"L. Tang","doi":"10.47443/dml.2023.148","DOIUrl":"https://doi.org/10.47443/dml.2023.148","url":null,"abstract":"We investigate several measures of peripherality for vertices and edges in networks. We improve asymptotic bounds on the maximum value achieved by edge peripherality, edge sum peripherality, and the Trinajsti'c index over $n$ vertex graphs. We also prove similar results on the maxima over $n$-vertex bipartite graphs, trees, and graphs with a fixed diameter. Finally, we refute two conjectures of Furtula, the first on necessary conditions for minimizing the Trinajsti'c index and the second about maximizing the Trinajsti'c index.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139368242","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
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