Pub Date : 2023-08-14DOI: 10.1080/00029890.2023.2242042
P. Renteln
We give a short combinatorial proof based on the Murnaghan-Nakayama rule of the symmetric group character identity χ λ χ (1 n ) = χ λ (cid:48) , where λ (cid:48) is the conjugate of the partition λ .
{"title":"A Combinatorial Proof of a Symmetric Group Character Involution","authors":"P. Renteln","doi":"10.1080/00029890.2023.2242042","DOIUrl":"https://doi.org/10.1080/00029890.2023.2242042","url":null,"abstract":"We give a short combinatorial proof based on the Murnaghan-Nakayama rule of the symmetric group character identity χ λ χ (1 n ) = χ λ (cid:48) , where λ (cid:48) is the conjugate of the partition λ .","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48149307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-14DOI: 10.1080/00029890.2023.2240266
Tom Moshaiov
{"title":"The Determinant Mod p of a Circulant Matrix of Order pm","authors":"Tom Moshaiov","doi":"10.1080/00029890.2023.2240266","DOIUrl":"https://doi.org/10.1080/00029890.2023.2240266","url":null,"abstract":"","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47027254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-14DOI: 10.1080/00029890.2023.2242039
D. Kalman, R. Mena
Abstract We formulate the Euclidean algorithm using directed graphs on integer points in the plane and operations on a particular semigroup of two by two matrices. The properties of the graphs and the semigroup provide surprisingly effective tools for solving certain classical diophantine equations, among other applications.
{"title":"A Tale of Two by Two Matrices","authors":"D. Kalman, R. Mena","doi":"10.1080/00029890.2023.2242039","DOIUrl":"https://doi.org/10.1080/00029890.2023.2242039","url":null,"abstract":"Abstract We formulate the Euclidean algorithm using directed graphs on integer points in the plane and operations on a particular semigroup of two by two matrices. The properties of the graphs and the semigroup provide surprisingly effective tools for solving certain classical diophantine equations, among other applications.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46035694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-14DOI: 10.1080/00029890.2023.2242046
Vadim Ponomarenko
"100 Years Ago This Month in the American Mathematical Monthly." The American Mathematical Monthly, ahead-of-print(ahead-of-print), p. 1
"100年前的这个月，美国数学月刊"《美国数学月刊》，印刷前，第1页
{"title":"100 Years Ago This Month in <i>the American Mathematical Monthly</i>","authors":"Vadim Ponomarenko","doi":"10.1080/00029890.2023.2242046","DOIUrl":"https://doi.org/10.1080/00029890.2023.2242046","url":null,"abstract":"\"100 Years Ago This Month in the American Mathematical Monthly.\" The American Mathematical Monthly, ahead-of-print(ahead-of-print), p. 1","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135214691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-14DOI: 10.1080/00029890.2023.2240233
Deanna B. Haunsperger
Abstract Mathematical communities which support women and members of underrepresented groups in mathematics can increase the likelihood of their earning advanced degrees in mathematics. Mathematicians should be investing more time, energy, and funding into supporting mathematical communities that exist and creating ones that are needed. Through the story of the Carleton Summer Mathematics Program for Women, we demonstrate that building such a community doesn’t need to be difficult, and it can be quite rewarding.
{"title":"Community and Belonging in Mathematics*","authors":"Deanna B. Haunsperger","doi":"10.1080/00029890.2023.2240233","DOIUrl":"https://doi.org/10.1080/00029890.2023.2240233","url":null,"abstract":"Abstract Mathematical communities which support women and members of underrepresented groups in mathematics can increase the likelihood of their earning advanced degrees in mathematics. Mathematicians should be investing more time, energy, and funding into supporting mathematical communities that exist and creating ones that are needed. Through the story of the Carleton Summer Mathematics Program for Women, we demonstrate that building such a community doesn’t need to be difficult, and it can be quite rewarding.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49097825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-14DOI: 10.1080/00029890.2023.2241336
G. Domokos, F. Kovács
Abstract We show an explicit construction in three dimensions for a convex, mono-monostatic polyhedron (i.e., having exactly one stable and one unstable equilibrium) with 21 vertices and 21 faces. This polyhedron is a 0-skeleton, with equal masses located at each vertex. The above construction serves as an upper bound for the minimal number of faces and vertices of mono-monostatic 0-skeletons and complements the recently provided lower bound of 8 vertices. This is the first known construction of a mono-monostatic polyhedral solid. We also show that a similar construction for homogeneous distribution of mass cannot result in a mono-monostatic solid.
{"title":"Conway’s Spiral and a Discrete Gömböc with 21 Point Masses","authors":"G. Domokos, F. Kovács","doi":"10.1080/00029890.2023.2241336","DOIUrl":"https://doi.org/10.1080/00029890.2023.2241336","url":null,"abstract":"Abstract We show an explicit construction in three dimensions for a convex, mono-monostatic polyhedron (i.e., having exactly one stable and one unstable equilibrium) with 21 vertices and 21 faces. This polyhedron is a 0-skeleton, with equal masses located at each vertex. The above construction serves as an upper bound for the minimal number of faces and vertices of mono-monostatic 0-skeletons and complements the recently provided lower bound of 8 vertices. This is the first known construction of a mono-monostatic polyhedral solid. We also show that a similar construction for homogeneous distribution of mass cannot result in a mono-monostatic solid.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49179174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-14DOI: 10.1080/00029890.2023.2231825
Daniel H. Ullman, Daniel J. Velleman, Stan Wagon, Douglas B. West
{"title":"Problems and Solutions","authors":"Daniel H. Ullman, Daniel J. Velleman, Stan Wagon, Douglas B. West","doi":"10.1080/00029890.2023.2231825","DOIUrl":"https://doi.org/10.1080/00029890.2023.2231825","url":null,"abstract":"","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135214391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-10DOI: 10.1080/00029890.2023.2240683
Shibo Liu
Abstract This paper presents an induction proof of the G-N-S inequality when p = 1, which the author believes is much simpler and more transparent than other proofs found in the literature.
{"title":"Gagliardo-Nirenberg-Sobolev Inequality: An Induction Proof","authors":"Shibo Liu","doi":"10.1080/00029890.2023.2240683","DOIUrl":"https://doi.org/10.1080/00029890.2023.2240683","url":null,"abstract":"Abstract This paper presents an induction proof of the G-N-S inequality when p = 1, which the author believes is much simpler and more transparent than other proofs found in the literature.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44822927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-04DOI: 10.1080/00029890.2023.2207417
Paul R. Halmos–Lester, R. Ford, P. Halmos, L. R. Ford
• Tristram Bogart & Kevin Woods (2022). A Plethora of Polynomials: A Toolbox for Counting Problems. Amer. Math. Monthly. 129(3): 203–222. • Paul Thomas Young (2022). From Madhava-Leibniz to Lehmer’s Limit. Amer. Math. Monthly. 129(6): 524–538. • Alex Rice (2022). Reciprocal Sums and Counting Functions. Amer. Math. Monthly. 129(10): 903–912. • Paul Ramond (2022). The Abel–Ruffini Theorem: Complex but Not Complicated. Amer. Math. Monthly. 129(3): 231–245
•Tristram Bogart和Kevin Woods（2022）。多项式丛：计算问题的工具箱。Amer。数学月刊129（3）：203–222。•Paul Thomas Young（2022）。从Madhava Leibniz到Lehmer极限。Amer。数学月刊129（6）：524–538。•Alex Rice（2022）。倒数和计数函数。Amer。数学月刊129（10）：903–912。•Paul Ramond（2022）。Abel–Ruffini定理：复杂但不复杂。Amer。数学月刊129（3）：231–245
{"title":"The Paul R. Halmos–Lester R. Ford Awards for 2022","authors":"Paul R. Halmos–Lester, R. Ford, P. Halmos, L. R. Ford","doi":"10.1080/00029890.2023.2207417","DOIUrl":"https://doi.org/10.1080/00029890.2023.2207417","url":null,"abstract":"• Tristram Bogart & Kevin Woods (2022). A Plethora of Polynomials: A Toolbox for Counting Problems. Amer. Math. Monthly. 129(3): 203–222. • Paul Thomas Young (2022). From Madhava-Leibniz to Lehmer’s Limit. Amer. Math. Monthly. 129(6): 524–538. • Alex Rice (2022). Reciprocal Sums and Counting Functions. Amer. Math. Monthly. 129(10): 903–912. • Paul Ramond (2022). The Abel–Ruffini Theorem: Complex but Not Complicated. Amer. Math. Monthly. 129(3): 231–245","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49141612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-04DOI: 10.1080/00029890.2023.2190724
Vesta Coufal, Suzanne Dorée, T. Dray, Frank Farris, Amy Shell-Gellasch, Derek Smith
The Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Mathematics is the most prestigious award for service offered by the Mathematical Association of America. It celebrates contributions to the community that have influenced the field of mathematics in a significant and positive way. Victor Katz
{"title":"Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2023 to Victor J. Katz for Distinguished Service to Mathematics","authors":"Vesta Coufal, Suzanne Dorée, T. Dray, Frank Farris, Amy Shell-Gellasch, Derek Smith","doi":"10.1080/00029890.2023.2190724","DOIUrl":"https://doi.org/10.1080/00029890.2023.2190724","url":null,"abstract":"The Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Mathematics is the most prestigious award for service offered by the Mathematical Association of America. It celebrates contributions to the community that have influenced the field of mathematics in a significant and positive way. Victor Katz","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45314360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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