Bulletin of the London Mathematical Society最新文献

{"title":"Orthogonal almost complex structure and its Nijenhuis tensor","authors":"Zizhou Tang, Wenjiao Yan","doi":"10.1112/blms.70044","DOIUrl":"https://doi.org/10.1112/blms.70044","url":null,"abstract":"<p>In this paper, we demonstrate that on an almost Hermitian manifold <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>M</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>,</mo>\u0000 <mi>J</mi>\u0000 <mo>,</mo>\u0000 <mi>d</mi>\u0000 <msup>\u0000 <mi>s</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(M^{2n}, J, ds^2)$</annotation>\u0000 </semantics></math>, a 2-form <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>φ</mi>\u0000 <mo>=</mo>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <mi>Φ</mi>\u0000 </mrow>\u0000 <annotation>$varphi =S^*Phi$</annotation>\u0000 </semantics></math>, the pullback of the Kähler form <span></span><math>\u0000 <semantics>\u0000 <mi>Φ</mi>\u0000 <annotation>$Phi$</annotation>\u0000 </semantics></math> on the twistor bundle over <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>M</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$M^{2n}$</annotation>\u0000 </semantics></math>, is nondegenerate if the squared norm <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mi>N</mi>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$|N|^2$</annotation>\u0000 </semantics></math> of the Nijenhuis tensor is less than <span></span><math>\u0000 <semantics>\u0000 <mfrac>\u0000 <mn>64</mn>\u0000 <mn>5</mn>\u0000 </mfrac>\u0000 <annotation>$frac{64}{5}$</annotation>\u0000 </semantics></math> when <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$ngeqslant 3$</annotation>\u0000 </semantics></math> or less than 16 when <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$n=2$</annotation>\u0000 </semantics></math>. As one of the consequences, there exists no orthogonal almost complex structure on the standard sphere <span></span><math>\u0000 <sem","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 5","pages":"1512-1523"},"PeriodicalIF":0.8,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143938905","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}

{"title":"The Baby Monster is the largest group with at most 2 irreducible characters with the same degree","authors":"Juan Martínez Madrid","doi":"10.1112/blms.70040","DOIUrl":"https://doi.org/10.1112/blms.70040","url":null,"abstract":"<p>We classify all finite groups such that all irreducible character degrees appear with multiplicity at most 2. As a consequence, we prove that the largest group with at most two irreducible characters of the same degree is the Baby Monster.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 5","pages":"1453-1467"},"PeriodicalIF":0.8,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143938975","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}

{"title":"Equality of skew Schur functions in noncommuting variables","authors":"Emma Yu Jin,&nbsp;Stephanie van Willigenburg","doi":"10.1112/blms.70037","DOIUrl":"https://doi.org/10.1112/blms.70037","url":null,"abstract":"&lt;p&gt;The question of classifying when two skew Schur functions are equal is a substantial open problem, which remains unsolved for over a century. In 2022, Aliniaeifard, Li, and van Willigenburg introduced skew Schur functions in noncommuting variables, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$s_{(delta,mathcal {D})}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {D}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a connected skew diagram with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;annotation&gt;$n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; boxes and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;annotation&gt;$delta$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a permutation in the symmetric group &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$S_n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. In this paper, we combine these two and classify when two skew Schur functions in noncommuting variables are equal: &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;τ&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$s_{(delta,mathcal {D})} = s_{(tau,mathcal {T})}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; such that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;mo&gt;≠&lt;/mo&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathcal {D}ne mathcal {T}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; if and only if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 5","pages":"1415-1428"},"PeriodicalIF":0.8,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70037","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143938740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Two results on the Convex Algebraic Geometry of sets with continuous symmetries","authors":"Renato G. Bettiol,&nbsp;Mario Kummer,&nbsp;Ricardo A. E. Mendes","doi":"10.1112/blms.70035","DOIUrl":"https://doi.org/10.1112/blms.70035","url":null,"abstract":"<p>We prove two results on convex subsets of Euclidean spaces invariant under an orthogonal group action. First, we show that invariant spectrahedra admit an equivariant spectrahedral description, that is, can be described by an equivariant linear matrix inequality. Second, we show that the bijection induced by Kostant's Convexity Theorem between convex subsets invariant under a polar representation and convex subsets of a section invariant under the Weyl group preserves the classes of convex semialgebraic sets, spectrahedral shadows, and rigidly convex sets.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 5","pages":"1388-1408"},"PeriodicalIF":0.8,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143938739","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}

{"title":"Closed \u0000 \u0000 \u0000 G\u0000 2\u0000 \u0000 $G_2$\u0000 -structures with negative Ricci curvature","authors":"Alec Payne","doi":"10.1112/blms.70029","DOIUrl":"https://doi.org/10.1112/blms.70029","url":null,"abstract":"<p>We study existence problems for closed <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$G_2$</annotation>\u0000 </semantics></math>-structures with negative Ricci curvature, and we prove the <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$G_2$</annotation>\u0000 </semantics></math>-Goldberg conjecture for noncompact manifolds. We first show that no closed manifold admits a closed <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$G_2$</annotation>\u0000 </semantics></math>-structure with negative Ricci curvature. In the noncompact setting, we show that no complete manifold admits a closed <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$G_2$</annotation>\u0000 </semantics></math>-structure with Ricci curvature pinched sufficiently close to a negative constant. As a consequence, an Einstein closed <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$G_2$</annotation>\u0000 </semantics></math>-structure on a complete manifold must be torsion-free. In addition, when the Einstein metric is incomplete, we find restrictions on lengths of geodesics.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 4","pages":"1270-1284"},"PeriodicalIF":0.8,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143835875","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}

{"title":"A higher dimensional version of Fáry's theorem","authors":"Karim Adiprasito,&nbsp;Zuzana Patáková","doi":"10.1112/blms.70036","DOIUrl":"https://doi.org/10.1112/blms.70036","url":null,"abstract":"<p>We prove a generalization of István Fáry's celebrated theorem to higher dimensions. Namely, we show that if a finite simplicial complex <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> can be piecewise linearly embedded into a <span></span><math>\u0000 <semantics>\u0000 <mi>d</mi>\u0000 <annotation>$d$</annotation>\u0000 </semantics></math>-dimensional PL manifold <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math>, then there is a triangulation of <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> containing <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> as a subcomplex.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 5","pages":"1409-1414"},"PeriodicalIF":0.8,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70036","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143939330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rigidity of proper holomorphic maps between nonequidimensional Fock–Bargmann–Hartogs domains","authors":"Guicong Su,&nbsp;Lei Wang","doi":"10.1112/blms.70038","DOIUrl":"https://doi.org/10.1112/blms.70038","url":null,"abstract":"<p>In this article, we introduce a novel rigidity theorem that investigates proper holomorphic maps between Fock–Bargmann–Hartogs domains of varying dimensions. Unlike previous studies, this theorem does not impose any restrictions on the codimension. Our main result demonstrates that any such proper holomorphic map <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math> can be equivalently represented as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msqrt>\u0000 <mi>k</mi>\u0000 </msqrt>\u0000 <msub>\u0000 <mi>z</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mtext>…</mtext>\u0000 <mo>,</mo>\u0000 <msqrt>\u0000 <mi>k</mi>\u0000 </msqrt>\u0000 <msub>\u0000 <mi>z</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mtext>…</mtext>\u0000 <mo>,</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <msup>\u0000 <mi>w</mi>\u0000 <mi>k</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(sqrt {k} z_1,ldots, sqrt {k} z_n, 0,ldots, 0, w^k)$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math> is a positive integer.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 5","pages":"1429-1444"},"PeriodicalIF":0.8,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143939272","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}

{"title":"Finiteness properties and relatively hyperbolic groups","authors":"Harsh Patil","doi":"10.1112/blms.70039","DOIUrl":"https://doi.org/10.1112/blms.70039","url":null,"abstract":"<p>We show that properties <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <annotation>$F_n$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>F</mi>\u0000 <msub>\u0000 <mi>P</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$FP_n$</annotation>\u0000 </semantics></math> hold for a relatively hyperbolic group if and only if they hold for all the peripheral subgroups. As an application we show that there are at least countably many distinct quasi-isometry classes of one-ended non-amenable groups that are type <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <annotation>$F_n$</annotation>\u0000 </semantics></math> but not <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$F_{n+1}$</annotation>\u0000 </semantics></math> and similarly of type <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>F</mi>\u0000 <msub>\u0000 <mi>P</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$FP_n$</annotation>\u0000 </semantics></math> and not <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>F</mi>\u0000 <msub>\u0000 <mi>P</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$FP_{n+1}$</annotation>\u0000 </semantics></math> for all positive integers <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 5","pages":"1445-1452"},"PeriodicalIF":0.8,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70039","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143939608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A new upper bound for the growth factor in Gaussian elimination with complete pivoting","authors":"Ankit Bisain,&nbsp;Alan Edelman,&nbsp;John Urschel","doi":"10.1112/blms.70034","DOIUrl":"https://doi.org/10.1112/blms.70034","url":null,"abstract":"<p>The growth factor in Gaussian elimination measures how large the entries of an LU factorization can be relative to the entries of the original matrix. It is a key parameter in error estimates, and one of the most fundamental topics in numerical analysis. We produce an upper bound of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>n</mi>\u0000 <mrow>\u0000 <mn>0.2079</mn>\u0000 <mi>ln</mi>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>0.91</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$n^{0.2079 ln n +0.91}$</annotation>\u0000 </semantics></math> for the growth factor in Gaussian elimination with complete pivoting — the first improvement upon Wilkinson's original 1961 bound of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mspace></mspace>\u0000 <msup>\u0000 <mi>n</mi>\u0000 <mrow>\u0000 <mn>0.25</mn>\u0000 <mi>ln</mi>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>0.5</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$2 , n ^{0.25ln n +0.5}$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 5","pages":"1369-1387"},"PeriodicalIF":0.8,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70034","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143939610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lorentzian polynomials and the independence sequences of graphs","authors":"Amire Bendjeddou,&nbsp;Leonard Hardiman","doi":"10.1112/blms.70031","DOIUrl":"https://doi.org/10.1112/blms.70031","url":null,"abstract":"<p>We study the multivariate independence polynomials of graphs and the log-concavity of the coefficients of their univariate restrictions. Let <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <msub>\u0000 <mi>W</mi>\u0000 <mn>4</mn>\u0000 </msub>\u0000 </msub>\u0000 <annotation>$R_{W_4}$</annotation>\u0000 </semantics></math> be the operator defined on simple and undirected graphs which replaces each edge with a caterpillar of size 4. We prove that all graphs in the image of <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <msub>\u0000 <mi>W</mi>\u0000 <mn>4</mn>\u0000 </msub>\u0000 </msub>\u0000 <annotation>$R_{W_4}$</annotation>\u0000 </semantics></math> are what we call pre-Lorentzian, that is, their multivariate independence polynomial becomes Lorentzian after appropriate manipulations. In particular, as pre-Lorentzian graphs have log-concave (and therefore unimodal) independence sequences, our result makes progress on a conjecture of Alavi, Malde, Schwenk and Erdős which asks if the independence sequence of trees or forests is unimodal.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 4","pages":"1305-1323"},"PeriodicalIF":0.8,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143836308","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}