Examples and Counterexamples最新文献

{"title":"Assemblies as semigroups","authors":"Ulderico Dardano ,&nbsp;Bruno Dinis ,&nbsp;Giuseppina Terzo","doi":"10.1016/j.exco.2024.100143","DOIUrl":"https://doi.org/10.1016/j.exco.2024.100143","url":null,"abstract":"<div><p>In this paper we give an algebraic characterization of assemblies in terms of bands of groups. We also consider substructures and homomorphisms of assemblies. We give many examples and counterexamples.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"5 ","pages":"Article 100143"},"PeriodicalIF":0.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X24000090/pdfft?md5=cb668f90949bc416ea00c880ec4aa3e0&pid=1-s2.0-S2666657X24000090-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140180647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A closer look at some new lower bounds on the minimum singular value of a matrix","authors":"Avleen Kaur ,&nbsp;S.H. Lui","doi":"10.1016/j.exco.2024.100142","DOIUrl":"https://doi.org/10.1016/j.exco.2024.100142","url":null,"abstract":"<div><p>There is an extensive body of literature on estimating the eigenvalues of the sum of two symmetric matrices, <span><math><mrow><mi>P</mi><mo>+</mo><mi>Q</mi></mrow></math></span>, in relation to the eigenvalues of <span><math><mi>P</mi></math></span> and <span><math><mi>Q</mi></math></span>. Recently, the authors introduced two novel lower bounds on the minimum eigenvalue, <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mo>min</mo></mrow></msub><mrow><mo>(</mo><mi>P</mi><mo>+</mo><mi>Q</mi><mo>)</mo></mrow></mrow></math></span>, under the conditions that matrices <span><math><mi>P</mi></math></span> and <span><math><mi>Q</mi></math></span> are symmetric positive semi-definite and their sum <span><math><mrow><mi>P</mi><mo>+</mo><mi>Q</mi></mrow></math></span> is non-singular. These bounds rely on the Friedrichs angle between the range spaces of matrices <span><math><mi>P</mi></math></span> and <span><math><mi>Q</mi></math></span>, which are denoted by <span><math><mrow><mi>R</mi><mrow><mo>(</mo><mi>P</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>R</mi><mrow><mo>(</mo><mi>Q</mi><mo>)</mo></mrow></mrow></math></span>, respectively. In addition, both results led to the derivation of several new lower bounds on the minimum singular value of full-rank matrices. One significant aspect of the two novel lower bounds on <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mo>min</mo></mrow></msub><mrow><mo>(</mo><mi>P</mi><mo>+</mo><mi>Q</mi><mo>)</mo></mrow></mrow></math></span> is the distinction of the case where <span><math><mrow><mi>R</mi><mrow><mo>(</mo><mi>P</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>R</mi><mrow><mo>(</mo><mi>Q</mi><mo>)</mo></mrow></mrow></math></span> have no principal angles between 0 and <span><math><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>. This work offers an explanation for the aforementioned scenario and presents a classification of all matrices that meet the specified criteria. Additionally, we offer insight into the rationale behind selecting the decomposition for the subspace <span><math><mrow><mi>R</mi><mrow><mo>(</mo><mi>Q</mi><mo>)</mo></mrow></mrow></math></span>, which is employed to formulate the lower bounds for <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mo>min</mo></mrow></msub><mrow><mo>(</mo><mi>P</mi><mo>+</mo><mi>Q</mi><mo>)</mo></mrow></mrow></math></span>. At last, an example that showcases the potential for improving these two lower bounds is presented.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"5 ","pages":"Article 100142"},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X24000089/pdfft?md5=0c2ae22f7c329a636b6ee13795d2840d&pid=1-s2.0-S2666657X24000089-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139985367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The locating chromatic number of generalized Petersen graphs with small order","authors":"Redha Sakri ,&nbsp;Moncef Abbas","doi":"10.1016/j.exco.2024.100141","DOIUrl":"https://doi.org/10.1016/j.exco.2024.100141","url":null,"abstract":"<div><p>It was conjectured by Asmiati (2018) that the generalized Petersen graph <span><math><mrow><mi>P</mi><mfenced><mrow><mi>n</mi><mo>,</mo><mi>k</mi></mrow></mfenced></mrow></math></span> has a locating chromatic number 4 if and only if <span><math><mrow><mo>(</mo><mi>n</mi><mspace></mspace><mi>o</mi><mi>d</mi><mi>d</mi><mspace></mspace><mi>a</mi><mi>n</mi><mi>d</mi><mspace></mspace><mi>k</mi><mo>=</mo><mn>1</mn><mo>)</mo></mrow></math></span> or <span><math><mrow><mo>(</mo><mi>n</mi><mo>=</mo><mn>4</mn><mspace></mspace><mi>a</mi><mi>n</mi><mi>d</mi><mspace></mspace><mi>k</mi><mo>=</mo><mn>2</mn><mo>)</mo></mrow></math></span>. In this paper, we give a negative answer to the conjecture posed by Asmiati. As a consequence, we are able to exhibit many counterexamples to the recent conjecture proposed, by proving that if <span><math><mrow><mo>(</mo><mn>5</mn><mo>≤</mo><mi>n</mi><mo>≤</mo><mn>12</mn><mo>)</mo></mrow></math></span> and <span><math><mrow><mo>(</mo><mn>2</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mrow><mo>⌊</mo><mfrac><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌋</mo></mrow><mo>)</mo></mrow></math></span> and <span><math><mrow><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow><mo>≠</mo><mrow><mo>(</mo><mn>12</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></mrow></math></span>, then <span><math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><msub><mrow></mrow><mrow><mi>L</mi></mrow></msub></mrow></msub><mfenced><mrow><mi>P</mi><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></mrow></mfenced><mo>=</mo><mn>4</mn></mrow></math></span>.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"5 ","pages":"Article 100141"},"PeriodicalIF":0.0,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X24000077/pdfft?md5=0c1ce0bbc9c76ab3ef2eb212405914a8&pid=1-s2.0-S2666657X24000077-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139898722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Trifferent codes with small lengths","authors":"Sascha Kurz","doi":"10.1016/j.exco.2024.100139","DOIUrl":"https://doi.org/10.1016/j.exco.2024.100139","url":null,"abstract":"<div><p>A code <span><math><mrow><mi>C</mi><mo>⊆</mo><msup><mrow><mrow><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></mrow></mrow><mrow><mi>n</mi></mrow></msup></mrow></math></span> of length <span><math><mi>n</mi></math></span> is called trifferent if for any three distinct elements of <span><math><mi>C</mi></math></span> there exists a coordinate in which they all differ. By <span><math><mrow><mi>T</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span> we denote the maximum cardinality of trifferent codes with length <span><math><mi>n</mi></math></span>. The values <span><math><mrow><mi>T</mi><mrow><mo>(</mo><mn>5</mn><mo>)</mo></mrow><mo>=</mo><mn>10</mn></mrow></math></span> and <span><math><mrow><mi>T</mi><mrow><mo>(</mo><mn>6</mn><mo>)</mo></mrow><mo>=</mo><mn>13</mn></mrow></math></span> were recently determined (Fiore et al., 2022). Here we determine <span><math><mrow><mi>T</mi><mrow><mo>(</mo><mn>7</mn><mo>)</mo></mrow><mo>=</mo><mn>16</mn></mrow></math></span>, <span><math><mrow><mi>T</mi><mrow><mo>(</mo><mn>8</mn><mo>)</mo></mrow><mo>=</mo><mn>20</mn></mrow></math></span>, and <span><math><mrow><mi>T</mi><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow><mo>=</mo><mn>27</mn></mrow></math></span>. For the latter case <span><math><mrow><mi>n</mi><mo>=</mo><mn>9</mn></mrow></math></span> there also exist linear codes attaining the maximum possible cardinality 27.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"5 ","pages":"Article 100139"},"PeriodicalIF":0.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X24000053/pdfft?md5=6d4ca67bb2a4151b63492ee97290bf7c&pid=1-s2.0-S2666657X24000053-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139699378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exploration of novel analytical solutions of boundary layer equation via the modified sumudu transform","authors":"Shailesh A. Bhanotar","doi":"10.1016/j.exco.2024.100140","DOIUrl":"https://doi.org/10.1016/j.exco.2024.100140","url":null,"abstract":"<div><p>The research introduces the Modified Sumudu Decomposition Method (MSDM) as a novel approach for solving non-linear ordinary differential equations. Stemming from the Sumudu Transformation (ST), proposed by Watugala in the 1990s, MSDM demonstrates its efficacy through the solution of a specific third-order non-homogeneous nonlinear ordinary differential equation. This method is particularly highlighted for its application in fluid mechanics, specifically addressing a boundary layer problem. Furthermore, the study employs Pade´ Approximants to evaluate a crucial parameter, ρ=φ''(0), and compares the results with other established methods, including Modified Laplace Decomposition Method (MLDM), Modified Adomian Decomposition Method (MADM), Modified Variational Iteration Method (MVIM), and the Homotopy Perturbation Method (HPM). The findings not only contribute to the advancement of mathematical techniques for solving complex differential equations but also provide a comparative analysis, elucidating the strengths and limitations of different methodologies. This research is anticipated to have significant implications for researchers and practitioners in the field, offering a valuable toolkit for tackling a wide range of mathematical modeling challenges.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"5 ","pages":"Article 100140"},"PeriodicalIF":0.0,"publicationDate":"2024-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X24000065/pdfft?md5=1031fe8a65f66ccd5bb3e0c15042941d&pid=1-s2.0-S2666657X24000065-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139714721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An arithmetic term for the factorial function","authors":"Mihai Prunescu ,&nbsp;Lorenzo Sauras-Altuzarra","doi":"10.1016/j.exco.2024.100136","DOIUrl":"https://doi.org/10.1016/j.exco.2024.100136","url":null,"abstract":"<div><p>As proved by Marchenkov and Mazzanti, every Kalmar function can be represented by arithmetic terms. We display one of such terms to represent the factorial function, and as a consequence, we get an example of an arithmetic term which represents a function whose image is the set of primes.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"5 ","pages":"Article 100136"},"PeriodicalIF":0.0,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X24000028/pdfft?md5=14034c2031c53802d6653cf6837b9961&pid=1-s2.0-S2666657X24000028-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139674621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ree groups as automorphism groups of block designs","authors":"Ashraf Daneshkhah","doi":"10.1016/j.exco.2024.100137","DOIUrl":"https://doi.org/10.1016/j.exco.2024.100137","url":null,"abstract":"<div><p>A recent classification of flag-transitive 2-designs with parameters <span><math><mrow><mo>(</mo><mi>v</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>λ</mi><mo>)</mo></mrow></math></span> whose replication number <span><math><mi>r</mi></math></span> is coprime to <span><math><mi>λ</mi></math></span> gives rise to eight possible infinite families of 2-designs, some of which are with new parameters. In this note, we give explicit constructions for two of these families of 2-designs, and show that for a given positive integer <span><math><mrow><mi>q</mi><mo>=</mo><msup><mrow><mn>3</mn></mrow><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>⩾</mo><mn>27</mn></mrow></math></span>, there exist 2-designs with parameters <span><math><mrow><mo>(</mo><msup><mrow><mi>q</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>+</mo><mn>1</mn><mo>,</mo><msup><mrow><mi>q</mi></mrow><mrow><mi>i</mi></mrow></msup><mo>,</mo><msup><mrow><mi>q</mi></mrow><mrow><mi>i</mi></mrow></msup><mo>−</mo><mn>1</mn><mo>)</mo></mrow></math></span>, for <span><math><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></math></span>, admitting the Ree group <span><math><mrow><msup><mrow></mrow><mrow><mn>2</mn></mrow></msup><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></mrow></math></span> as their automorphism groups.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"5 ","pages":"Article 100137"},"PeriodicalIF":0.0,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X2400003X/pdfft?md5=874ac10905c9399343d40e6310933a30&pid=1-s2.0-S2666657X2400003X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139674623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Infinite families of trees with equal spectral radius","authors":"Francesco Belardo,&nbsp;Maurizio Brunetti","doi":"10.1016/j.exco.2024.100138","DOIUrl":"https://doi.org/10.1016/j.exco.2024.100138","url":null,"abstract":"<div><p>In this note we show that for each positive integer <span><math><mrow><mi>a</mi><mo>⩾</mo><mn>2</mn></mrow></math></span> there exist infinitely many trees whose spectral radius is equal to <span><math><msqrt><mrow><mn>2</mn><mi>a</mi></mrow></msqrt></math></span>. Such trees are obtained by replacing the central edge of the double star <span><math><mrow><mi>S</mi><mrow><mo>(</mo><mi>a</mi><mo>,</mo><mn>2</mn><mi>a</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> with suitable bidegreed caterpillars.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"5 ","pages":"Article 100138"},"PeriodicalIF":0.0,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X24000041/pdfft?md5=163e05dcfa0673ec0b2a9629bf2ab099&pid=1-s2.0-S2666657X24000041-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139674622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Corrigendum to “On the conjecture of Sombor energy of a graph” [Examples and Counterexamples 3 (2023) 100115]","authors":"Harishchandra S. Ramane ,&nbsp;Deepa V. Kitturmath","doi":"10.1016/j.exco.2024.100135","DOIUrl":"https://doi.org/10.1016/j.exco.2024.100135","url":null,"abstract":"<div><p>In this corrigendum, we correct some errors in the proof of Theorem 2.1 in “On the conjecture of Sombor energy of a graph” [Examples and Counterexamples 3 (2023) 100115].</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"5 ","pages":"Article 100135"},"PeriodicalIF":0.0,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X24000016/pdfft?md5=9eaf8b07dc7392eca6de0037bd6665cc&pid=1-s2.0-S2666657X24000016-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139653566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A note on non-supercyclic vectors of Hilbert space operators","authors":"Masoumeh Faghih-Ahmadi,&nbsp;Karim Hedayatian","doi":"10.1016/j.exco.2023.100131","DOIUrl":"https://doi.org/10.1016/j.exco.2023.100131","url":null,"abstract":"<div><p>In this note it is shown that there is a bounded linear operator <span><math><mi>T</mi></math></span> on the Hardy Hilbert space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and a vector <span><math><mi>f</mi></math></span> in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> such that the closure of the set <span><math><mrow><mo>{</mo><mi>α</mi><msup><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msup><mi>f</mi><mo>:</mo><mi>α</mi><mo>∈</mo><mi>ℂ</mi><mo>,</mo><mspace></mspace><mi>n</mi><mo>≥</mo><mn>0</mn><mo>}</mo></mrow></math></span> is not <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, but for every subsequence <span><math><msubsup><mrow><mrow><mo>(</mo><msub><mrow><mi>n</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>∞</mi></mrow></msubsup></math></span> the closed linear span of <span><math><mrow><mo>{</mo><msup><mrow><mi>T</mi></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></msup><mi>f</mi><mo>:</mo><mi>k</mi><mo>≥</mo><mn>1</mn><mo>}</mo></mrow></math></span> is the whole space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. Furthermore, the closure of <span><math><mrow><mo>{</mo><msup><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msup><mi>g</mi><mo>:</mo><mi>n</mi><mo>≥</mo><mn>0</mn><mo>}</mo></mrow></math></span> is <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> for some <span><math><mrow><mi>g</mi><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"5 ","pages":"Article 100131"},"PeriodicalIF":0.0,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X23000332/pdfft?md5=d5b92bb3f23309e6fdacec6aceef1367&pid=1-s2.0-S2666657X23000332-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139433408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}