Journal of Combinatorial Algebra最新文献_第3页

On additive bases in infinite abelian semigroups 无穷阿贝尔半群中的加性基

IF 0.9 2区数学

Journal of Combinatorial Algebra Pub Date : 2020-02-10 DOI: 10.4171/jca/67

Pierre-Yves Bienvenu, B. Girard, T. H. Lê

{"title":"On additive bases in infinite abelian semigroups","authors":"Pierre-Yves Bienvenu, B. Girard, T. H. Lê","doi":"10.4171/jca/67","DOIUrl":"https://doi.org/10.4171/jca/67","url":null,"abstract":"Building on previous work by Lambert, Plagne and the third author, we study various aspects of the behavior of additive bases in infinite abelian groups. We show that, for every such group $T$, the number of essential subsets of any additive basis is finite, and also that the number of essential subsets of cardinality $k$ contained in an additive basis of order at most $h$ can be bounded in terms of $h$ and $k$ alone. These results extend the reach of two theorems, one due to Deschamps and Farhi and the other to Hegarty, bearing upon $mathbf{N}$. Also, using invariant means, we address a classical problem, initiated by ErdH{o}s and Graham and then generalized by Nash and Nathanson both in the case of $mathbf{N}$, of estimating the maximal order $X_T(h,k)$ that a basis of cocardinality $k$ contained in an additive basis of order at most $h$ can have. Among other results, we prove that $X_T(h,k)=O(h^{2k+1})$ for every integer $k ge 1$. This result is new even in the case where $k=1$. Besides the maximal order $X_T(h,k)$, the typical order $S_T(h,k)$ is also studied. Our methods actually apply to a wider class of infinite abelian semigroups, thus unifying in a single axiomatic frame the theory of additive bases in $mathbf{N}$ and in abelian groups.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43578896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Defining relations for quantum symmetric pair coideals of Kac–Moody type 定义Kac-Moody型量子对称对共理想的关系

IF 0.9 2区数学

Journal of Combinatorial Algebra Pub Date : 2019-12-11 DOI: 10.4171/JCA/57

Hadewijch De Clercq

引用次数: 4

A generalization of combinatorial identities for stable discrete series constants 稳定离散序列常数组合恒等式的推广

IF 0.9 2区数学

Journal of Combinatorial Algebra Pub Date : 2019-12-01 DOI: 10.4171/jca/62

R. Ehrenborg, S. Morel, Margaret A. Readdy

{"title":"A generalization of combinatorial identities for stable discrete series constants","authors":"R. Ehrenborg, S. Morel, Margaret A. Readdy","doi":"10.4171/jca/62","DOIUrl":"https://doi.org/10.4171/jca/62","url":null,"abstract":"This article is concerned with the constants that appear in Harish-Chandra's character formula for stable discrete series of real reductive groups, although it does not require any knowledge about real reductive groups or discrete series. In Harish-Chandra's work the only information we have about these constants is that they are uniquely determined by an inductive property. Later Goresky--Kottwitz--MacPherson and Herb gave different formulas for these constants. In this article we generalize these formulas to the case of arbitrary finite Coxeter groups (in this setting, discrete series no longer make sense), and give a direct proof that the two formulas agree. We actually prove a slightly more general identity that also implies the combinatorial identity underlying discrete series character identities proved in a previous paper of the second author. We also introduce a signed convolution of valuations on polyhedral cones in Euclidean space and show that the resulting function is a valuation. This gives a theoretical framework for the valuation appearing in Appendix A of the Goresky--Kottwitz--MacPherson article. In Appendix B we extend the notion of $2$-structures (due to Herb) to pseudo-root systems.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47325081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Keys and Demazure crystals for Kac–Moody algebras Kac-Moody代数的键和Demazure晶体

IF 0.9 2区数学

Journal of Combinatorial Algebra Pub Date : 2019-09-20 DOI: 10.4171/jca/46

N. Jacon, C. Lecouvey

引用次数: 9

Flat deformations of algebras and functional equations 代数与函数方程的平面变形

IF 0.9 2区数学

Journal of Combinatorial Algebra Pub Date : 2019-09-17 DOI: 10.4171/jca/31

B. Feigin, Alexandre Odesski