Pub Date : 2023-06-15DOI: 10.4153/s0008414x23000391
Luka Milićević
{"title":"Quantitative Inverse Theorem for Gowers Uniformity Norms and in","authors":"Luka Milićević","doi":"10.4153/s0008414x23000391","DOIUrl":"https://doi.org/10.4153/s0008414x23000391","url":null,"abstract":"","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78810752","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}
Pub Date : 2023-06-14DOI: 10.4153/s0008414x23000378
K. Beanland, Hùng Việt Chu
{"title":"Schreier Families and -(almost) greedy bases","authors":"K. Beanland, Hùng Việt Chu","doi":"10.4153/s0008414x23000378","DOIUrl":"https://doi.org/10.4153/s0008414x23000378","url":null,"abstract":"","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"12 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84268565","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}
Pub Date : 2023-05-26DOI: 10.4153/s0008414x23000342
Luke Schaeffer, Jeffrey Shallit
Abstract We show that the first-order logical theory of the binary overlap-free words (and, more generally, the $alpha $ -free words for rational $alpha $ , $2 < alpha leq 7/3$ ), is decidable. As a consequence, many results previously obtained about this class through tedious case-based proofs can now be proved “automatically,” using a decision procedure, and new claims can be proved or disproved simply by restating them as logical formulas.
{"title":"The first-order theory of binary overlap-free words is decidable","authors":"Luke Schaeffer, Jeffrey Shallit","doi":"10.4153/s0008414x23000342","DOIUrl":"https://doi.org/10.4153/s0008414x23000342","url":null,"abstract":"Abstract We show that the first-order logical theory of the binary overlap-free words (and, more generally, the $alpha $ -free words for rational $alpha $ , $2 < alpha leq 7/3$ ), is decidable. As a consequence, many results previously obtained about this class through tedious case-based proofs can now be proved “automatically,” using a decision procedure, and new claims can be proved or disproved simply by restating them as logical formulas.","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"134 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135996842","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}
Pub Date : 2023-05-22DOI: 10.4153/s0008414x23000329
Xuan Kien Phung
Abstract For linear nonuniform cellular automata (NUCA) which are local perturbations of linear CA over a group universe G and a finite-dimensional vector space alphabet V over an arbitrary field k , we investigate their Dedekind finiteness property, also known as the direct finiteness property, i.e., left or right invertibility implies invertibility. We say that the group G is $L^1$ -surjunctive, resp. finitely $L^1$ -surjunctive, if all such linear NUCA are automatically surjective whenever they are stably injective, resp. when in addition k is finite. In parallel, we introduce the ring $D^1(k[G])$ which is the Cartesian product $k[G] times (k[G])[G]$ as an additive group but the multiplication is twisted in the second component. The ring $D^1(k[G])$ contains naturally the group ring $k[G]$ and we obtain a dynamical characterization of its stable finiteness for every field k in terms of the finite $L^1$ -surjunctivity of the group G , which holds, for example, when G is residually finite or initially subamenable. Our results extend known results in the case of CA.
{"title":"Stable finiteness of twisted group rings and noisy linear cellular automata","authors":"Xuan Kien Phung","doi":"10.4153/s0008414x23000329","DOIUrl":"https://doi.org/10.4153/s0008414x23000329","url":null,"abstract":"Abstract For linear nonuniform cellular automata (NUCA) which are local perturbations of linear CA over a group universe G and a finite-dimensional vector space alphabet V over an arbitrary field k , we investigate their Dedekind finiteness property, also known as the direct finiteness property, i.e., left or right invertibility implies invertibility. We say that the group G is $L^1$ -surjunctive, resp. finitely $L^1$ -surjunctive, if all such linear NUCA are automatically surjective whenever they are stably injective, resp. when in addition k is finite. In parallel, we introduce the ring $D^1(k[G])$ which is the Cartesian product $k[G] times (k[G])[G]$ as an additive group but the multiplication is twisted in the second component. The ring $D^1(k[G])$ contains naturally the group ring $k[G]$ and we obtain a dynamical characterization of its stable finiteness for every field k in terms of the finite $L^1$ -surjunctivity of the group G , which holds, for example, when G is residually finite or initially subamenable. Our results extend known results in the case of CA.","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135337986","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}
Pub Date : 2023-05-11DOI: 10.4153/s0008414x2300024x
{"title":"CJM volume 75 issue 3 Cover and Front matter","authors":"","doi":"10.4153/s0008414x2300024x","DOIUrl":"https://doi.org/10.4153/s0008414x2300024x","url":null,"abstract":"","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"4 1","pages":"f1 - f3"},"PeriodicalIF":0.7,"publicationDate":"2023-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84704974","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}
Pub Date : 2023-05-11DOI: 10.4153/s0008414x23000251
{"title":"CJM volume 75 issue 3 Cover and Back matter","authors":"","doi":"10.4153/s0008414x23000251","DOIUrl":"https://doi.org/10.4153/s0008414x23000251","url":null,"abstract":"","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"108 1","pages":"b1 - b2"},"PeriodicalIF":0.7,"publicationDate":"2023-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87634898","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}
Pub Date : 2023-05-02DOI: 10.4153/s0008414x23000299
I. Ishii, Takuji Nakamura, Toshio Saito
{"title":"A coloring invariant of 3-manifolds derived from their flow-spines and virtual knot diagrams","authors":"I. Ishii, Takuji Nakamura, Toshio Saito","doi":"10.4153/s0008414x23000299","DOIUrl":"https://doi.org/10.4153/s0008414x23000299","url":null,"abstract":"","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"34 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79611197","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}
Pub Date : 2023-04-24DOI: 10.4153/s0008414x23000275
D. Gorbachev, V. Ivanov, S. Tikhonov
{"title":"Logan’s problem for Jacobi transforms","authors":"D. Gorbachev, V. Ivanov, S. Tikhonov","doi":"10.4153/s0008414x23000275","DOIUrl":"https://doi.org/10.4153/s0008414x23000275","url":null,"abstract":"","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"6 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89286348","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}
Pub Date : 2023-03-27DOI: 10.4153/s0008414x23000196
M. Câmara, K. Kliś-Garlicka, M. Ptak
{"title":"GENERAL TOEPLITZ KERNELS AND –INVARIANCE","authors":"M. Câmara, K. Kliś-Garlicka, M. Ptak","doi":"10.4153/s0008414x23000196","DOIUrl":"https://doi.org/10.4153/s0008414x23000196","url":null,"abstract":"","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"20 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90172866","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}
Pub Date : 2023-03-20DOI: 10.4153/s0008414x23000147
{"title":"CJM volume 75 issue 2 Cover and Back matter","authors":"","doi":"10.4153/s0008414x23000147","DOIUrl":"https://doi.org/10.4153/s0008414x23000147","url":null,"abstract":"","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"23 1","pages":"b1 - b2"},"PeriodicalIF":0.7,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77769863","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}
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