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Generating Trees for 0021-Avoiding Inversion Sequences and a Conjecture of Hong and Li 0021-避免反转序列树的生成及Hong和Li的猜想
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-03-07 DOI: 10.47443/dml.2023.012
T. Mansour
{"title":"Generating Trees for 0021-Avoiding Inversion Sequences and a Conjecture of Hong and Li","authors":"T. Mansour","doi":"10.47443/dml.2023.012","DOIUrl":"https://doi.org/10.47443/dml.2023.012","url":null,"abstract":"An inversion sequence of length n is a word e = e 0 · · · e n which satisfies, for each i ∈ [ n ] = { 0 , 1 , . . . , n } , the inequality 0 ≤ e i ≤ i . In this paper, by generating tree tools, an explicit formula is found for the generating function for the number of inversion sequences of length n that avoid 0021 , which resolves the conjecture of Hong and Li posed in the recent paper [ Electron. J. Combin. 29 (2022) #4.37].","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43061525","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: 3
A new 4-chromatic edge critical Koester graph 一个新的四色边缘临界Koester图
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-03-07 DOI: 10.47443/dml.2022.166
A. Dobrynin
{"title":"A new 4-chromatic edge critical Koester graph","authors":"A. Dobrynin","doi":"10.47443/dml.2022.166","DOIUrl":"https://doi.org/10.47443/dml.2022.166","url":null,"abstract":"Let S be a decomposition of a simple 4-regular plane graph into edge-disjoint cycles such that every two adjacent edges on a face belong to different cycles of S . Such graphs, called Gr¨otzsch–Sachs graphs, may be considered as a result of a superposition of simple closed curves in the plane with tangencies disallowed. Koester studied the coloring of Gr¨otzsch– Sachs graphs when all curves are circles. In 1984, he presented the first example of a 4-chromatic edge critical plane graph of order 40 formed by 7 circles. In the present paper, a new 4-chromatic edge critical graph generated by circles in the plane is presented.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48052817","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
Hagen–Rothe Convolution Identities Through Lagrange Interpolations 拉格朗日插值的Hagen–Rothe卷积恒等式
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-03-03 DOI: 10.47443/dml.2022.188
W. Chu
{"title":"Hagen–Rothe Convolution Identities Through Lagrange Interpolations","authors":"W. Chu","doi":"10.47443/dml.2022.188","DOIUrl":"https://doi.org/10.47443/dml.2022.188","url":null,"abstract":"New proofs of Hagen–Rothe identities concerning binomial convolutions are presented through Lagrange interpolations. Keywords: Chu–Vandermonde formula; Hagen–Rothe identities; finite difference; Lagrange interpolation. 2020 Mathematics Subject Classification: 05A10, 11B65.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46933778","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
Recent Results on Hyperbolicity on Unitary Operators on Graphs 关于图上酉算子的双曲性的最新结果
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-03-03 DOI: 10.47443/dml.2022.179
Jes´us, A. M´endez, Rosalío Reyes, Jos´e M. Rodr´ıguez, J. M. Sigarreta
{"title":"Recent Results on Hyperbolicity on Unitary Operators on Graphs","authors":"Jes´us, A. M´endez, Rosalío Reyes, Jos´e M. Rodr´ıguez, J. M. Sigarreta","doi":"10.47443/dml.2022.179","DOIUrl":"https://doi.org/10.47443/dml.2022.179","url":null,"abstract":"For a geodesic metric space X and for x 1 , x 2 , x 3 ∈ X , a geodesic triangle T = { x 1 , x 2 , x 3 } is the union of the three geodesics [ x 1 x 2 ] , [ x 2 x 3 ] and [ x 3 x 1 ] in X . The space X is δ - hyperbolic (in Gromov sense) if any side of T is contained in a δ -neighborhood of the union of the two other sides, for every geodesic triangle T in X . If X is hyperbolic, we denote by δ ( X ) the sharp hyperbolicity constant of X , i.e., δ ( X ) := sup { δ ( T ) : T is a geodesic triangle in X } . In this paper, we collect previous results and prove new theorems on the hyperbolic constant of some important unitary operators on graphs","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49230952","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
S-Motzkin paths with catastrophes and air pockets s -莫兹金路径有灾难和气穴
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-02-14 DOI: 10.47443/dml.2023.052
H. Prodinger
{"title":"S-Motzkin paths with catastrophes and air pockets","authors":"H. Prodinger","doi":"10.47443/dml.2023.052","DOIUrl":"https://doi.org/10.47443/dml.2023.052","url":null,"abstract":"So called $S$-Motzkin paths are combined the concepts `catastrophes' and `air pockets. The enumeration is done by properly set up bivariate generating functions which can be extended using the kernel method.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48641690","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 the local antimagic chromatic number of the lexicographic product of graphs 论图的词典积的局部反幻色数
Discrete Mathematics Letters Pub Date : 2023-02-03 DOI: 10.47443/dml.2022.149
{"title":"On the local antimagic chromatic number of the lexicographic product of graphs","authors":"","doi":"10.47443/dml.2022.149","DOIUrl":"https://doi.org/10.47443/dml.2022.149","url":null,"abstract":"","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":"268 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135205999","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
Enumeration of r-smooth words over a finite alphabet 有限字母表上r个光滑词的枚举
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-02-01 DOI: 10.47443/dml.2022.175
T. Mansour, J. L. Ram´ırez, Diego Villamizar
{"title":"Enumeration of r-smooth words over a finite alphabet","authors":"T. Mansour, J. L. Ram´ırez, Diego Villamizar","doi":"10.47443/dml.2022.175","DOIUrl":"https://doi.org/10.47443/dml.2022.175","url":null,"abstract":"In this paper, we enumerate a restricted family of k -ary words called r -smooth words. The restriction is defined through the distance between adjacent changes in the word. Using automata, we enumerate this family of words. Additionally, we give explicit combinatorial expressions to enumerate the words and asymptotic expansions related to the Fibonacci sequence","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44706877","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
Some Observations on the Laplacian-Energy-Like Invariant of Trees 关于树的拉普拉斯类能不变量的一些观察
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-11-23 DOI: 10.47443/dml.2022.089
M. Matejic, S. Altindag, I. Milovanovic, E. Milovanovic
{"title":"Some Observations on the Laplacian-Energy-Like Invariant of Trees","authors":"M. Matejic, S. Altindag, I. Milovanovic, E. Milovanovic","doi":"10.47443/dml.2022.089","DOIUrl":"https://doi.org/10.47443/dml.2022.089","url":null,"abstract":"Let G be a graph of order n . Denote by A the adjacency matrix of G and by D = diag ( d 1 , . . . , d n ) the diagonal matrix of vertex degrees of G . The Laplacian matrix of G is defined as L = D − A . Let µ 1 , µ 2 , · · · , µ n − 1 , µ n be eigenvalues of L satisfying µ 1 ≥ µ 2 ≥ · · · ≥ µ n − 1 ≥ µ n = 0 . The Laplacian-energy–like invariant is a graph invariant defined as LEL ( G ) = (cid:80) n − 1 i =1 √ µ i . Improved upper bounds for LEL ( G ) are obtained and compared when G has a tree structure.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46187798","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
Linear Codes Over a General Infinite Family of Rings and Macwilliams-Type Relations 一般无限环族上的线性码与macwilliams型关系
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-11-23 DOI: 10.47443/dml.2022.091
Irwansyah, D. Suprijanto
{"title":"Linear Codes Over a General Infinite Family of Rings and Macwilliams-Type Relations","authors":"Irwansyah, D. Suprijanto","doi":"10.47443/dml.2022.091","DOIUrl":"https://doi.org/10.47443/dml.2022.091","url":null,"abstract":"We study structural properties of linear codes over the ring R k which is defined by R [ v 1 , v 2 , . . . , v k ] with conditions v 2 i = v i for i = 1 , 2 , . . . , k , where R is any finite commutative Frobenius ring. We describe these linear codes in terms of necessary and sufficient conditions involving Gray maps, and we use these characterizations to construct Hermitian and Euclidean self-dual linear codes of this ring of arbitrary given length. We also derive MacWilliams-type relations for these codes with respect to Hamming weight enumerator as well as complete and symmetrized weight enumerators. As an application of the obtained results, we construct several optimal linear codes over Z 4 .","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49106717","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
Principal Minors of Hermitian (Quasi-)Laplacian Matrix of Second Kind for Mixed Graphs 混合图的第二类厄米(拟)拉普拉斯矩阵的主次矩阵
IF 0.8
Discrete Mathematics Letters Pub Date : 2022-11-23 DOI: 10.47443/dml.2022.131
Qi Xiong, Gui-Xian Tian, Shu-Yu Cui
{"title":"Principal Minors of Hermitian (Quasi-)Laplacian Matrix of Second Kind for Mixed Graphs","authors":"Qi Xiong, Gui-Xian Tian, Shu-Yu Cui","doi":"10.47443/dml.2022.131","DOIUrl":"https://doi.org/10.47443/dml.2022.131","url":null,"abstract":"P.R","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47043139","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
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