Journal of Combinatorial Theory Series A最新文献

英文中文

Matroid Horn functions 矩阵角函数

IF 1.1 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2023-11-24 DOI: 10.1016/j.jcta.2023.105838

Kristóf Bérczi , Endre Boros , Kazuhisa Makino

Hypergraph Horn functions were introduced as a subclass of Horn functions that can be represented by a collection of circular implication rules. These functions possess distinguished structural and computational properties. In particular, their characterizations in terms of implicate-duality and the closure operator provide extensions of matroid duality and the Mac Lane – Steinitz exchange property of matroid closure, respectively.

In the present paper, we introduce a subclass of hypergraph Horn functions that we call matroid Horn functions. We provide multiple characterizations of matroid Horn functions in terms of their canonical and complete CNF representations. We also study the Boolean minimization problem for this class, where the goal is to find a minimum size representation of a matroid Horn function given by a CNF representation. While there are various ways to measure the size of a CNF, we focus on the number of circuits and circuit clauses. We determine the size of an optimal representation for binary matroids, and give lower and upper bounds in the uniform case. For uniform matroids, we show a strong connection between our problem and Turán systems that might be of independent combinatorial interest.

超图角函数是角函数的一个子类，可以用一组圆形隐含规则表示。这些函数具有独特的结构和计算特性。特别是，它们在隐含对偶性和闭包算子方面的描述分别提供了矩阵对偶性的扩展和矩阵闭包的Mac Lane - Steinitz交换性质。本文引入了超图角函数的一个子类，我们称之为矩阵角函数。我们根据矩阵角函数的正则和完全CNF表示，给出了矩阵角函数的多种表征。我们还研究了该类的布尔最小化问题，其目标是找到由CNF表示给出的矩阵Horn函数的最小大小表示。虽然有各种方法来测量CNF的大小，但我们主要关注电路和电路子句的数量。我们确定了二元拟阵的最优表示的大小，并给出了均匀情况下的下界和上界。对于一致拟阵，我们展示了我们的问题和Turán系统之间的紧密联系，这些系统可能具有独立的组合兴趣。

{"title":"Matroid Horn functions","authors":"Kristóf Bérczi , Endre Boros , Kazuhisa Makino","doi":"10.1016/j.jcta.2023.105838","DOIUrl":"https://doi.org/10.1016/j.jcta.2023.105838","url":null,"abstract":"<div>Hypergraph Horn functions were introduced as a subclass of Horn functions that can be represented by a collection of circular implication rules. These functions possess distinguished structural and computational properties. In particular, their characterizations in terms of implicate-duality and the closure operator provide extensions of matroid duality and the Mac Lane–Steinitz exchange property of matroid closure, respectively.In the present paper, we introduce a subclass of hypergraph Horn functions that we call matroid Horn functions. We provide multiple characterizations of matroid Horn functions in terms of their canonical and complete CNF representations. We also study the Boolean minimization problem for this class, where the goal is to find a minimum size representation of a matroid Horn function given by a CNF representation. While there are various ways to measure the size of a CNF, we focus on the number of circuits and circuit clauses. We determine the size of an optimal representation for binary matroids, and give lower and upper bounds in the uniform case. For uniform matroids, we show a strong connection between our problem and Turán systems that might be of independent combinatorial interest.</div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"203 ","pages":"Article 105838"},"PeriodicalIF":1.1,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0097316523001061/pdfft?md5=55c70db92d34f783b8e0189c2f8d7950&pid=1-s2.0-S0097316523001061-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138404270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Some refinements of Stanley's shuffle theorem 斯坦利洗牌定理的一些改进

IF 1.1 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2023-11-17 DOI: 10.1016/j.jcta.2023.105830

Kathy Q. Ji, Dax T.X. Zhang

We give a combinatorial proof of Stanley's shuffle theorem by using the insertion lemma of Haglund, Loehr and Remmel. Based on this combinatorial construction, we establish several refinements of Stanley's shuffle theorem.

利用Haglund, Loehr和Remmel的插入引理，给出Stanley洗牌定理的组合证明。基于这个组合构造，我们建立了斯坦利洗牌定理的几个改进。

引用次数: 0

The Clebsch–Gordan coefficients of U(sl2) and the Terwilliger algebras of Johnson graphs U(sl2)的Clebsch-Gordan系数和Johnson图的Terwilliger代数

IF 1.1 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2023-11-16 DOI: 10.1016/j.jcta.2023.105833

Hau-Wen Huang

<div>The universal enveloping algebra <math><mi>U</mi><mo>(</mo><msub><mrow><mi>sl</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math> of <math><msub><mrow><mi>sl</mi></mrow><mrow><mn>2</mn></mrow></msub></math> is a unital associative algebra over <math><mi>C</mi></math> generated by <math><mi>E</mi><mo>,</mo><mi>F</mi><mo>,</mo><mi>H</mi></math> subject to the relations<math><mrow><mo>[</mo><mi>H</mi><mo>,</mo><mi>E</mi><mo>]</mo><mo>=</mo><mn>2</mn><mi>E</mi><mo>,</mo><mspace></mspace><mo>[</mo><mi>H</mi><mo>,</mo><mi>F</mi><mo>]</mo><mo>=</mo><mo>−</mo><mn>2</mn><mi>F</mi><mo>,</mo><mspace></mspace><mo>[</mo><mi>E</mi><mo>,</mo><mi>F</mi><mo>]</mo><mo>=</mo><mi>H</mi><mo>.</mo></mrow></math> The element<math><mi>Λ</mi><mo>=</mo><mi>E</mi><mi>F</mi><mo>+</mo><mi>F</mi><mi>E</mi><mo>+</mo><mfrac><mrow><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn></mrow></mfrac></math> is called the Casimir element of <math><mi>U</mi><mo>(</mo><msub><mrow><mi>sl</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math>. Let <math><mi>Δ</mi><mo>:</mo><mi>U</mi><mo>(</mo><msub><mrow><mi>sl</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo><mo>→</mo><mi>U</mi><mo>(</mo><msub><mrow><mi>sl</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo><mo>⊗</mo><mi>U</mi><mo>(</mo><msub><mrow><mi>sl</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math> denote the comultiplication of <math><mi>U</mi><mo>(</mo><msub><mrow><mi>sl</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math>. The universal Hahn algebra <math><mi>H</mi></math> is a unital associative algebra over <math><mi>C</mi></math> generated by <math><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi></math> and the relations assert that <math><mo>[</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>]</mo><mo>=</mo><mi>C</mi></math> and each of<math><mrow><mo>[</mo><mi>C</mi><mo>,</mo><mi>A</mi><mo>]</mo><mo>+</mo><mn>2</mn><msup><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>B</mi><mo>,</mo><mspace></mspace><mo>[</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>]</mo><mo>+</mo><mn>4</mn><mi>B</mi><mi>A</mi><mo>+</mo><mn>2</mn><mi>C</mi></mrow></math> is central in <math><mi>H</mi></math>. Inspired by the Clebsch–Gordan coefficients of <math><mi>U</mi><mo>(</mo><msub><mrow><mi>sl</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math>, we discover an algebra homomorphism <math><mo>♮</mo><mo>:</mo><mi>H</mi><mo>→</mo><mi>U</mi><mo>(</mo><msub><mrow><mi>sl</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo><mo>⊗</mo><mi>U</mi><mo>(</mo><msub><mrow><mi>sl</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math> that maps<

sl2的泛包络代数U(sl2)是C上由E,F,H根据[H,E]=2E，[H,F]= - 2F，[E,F]=H生成的一元结合代数。elementΛ=EF+FE+H22称为U(sl2)的卡西米尔元素。设Δ:U(sl2)→U(sl2)⊗U(sl2)表示U(sl2)的乘法。通称Hahn代数H是由a,B,C生成的C上的一元结合代数，关系式表明[a,B]=C，且[C, a]+2A2+B，[B,C]+4BA+2C都在H的中心位置。根据U(sl2)的Clebsch-Gordan系数，我们发现了一个代数同态:H→U(sl2)⊗U(sl2)，它映射sa∈H⊗1−1⊗H4,B∈Δ(Λ)2,C∈E⊗F−F⊗E。通过缩回，任何U(sl2)⊗U(sl2)模都可以看作是h模。对于任意整数n≥0，存在一个唯一的(n+1)维不可约U(sl2)模Ln，直至同构。研究了任意整数m,n≥0时h模Lm⊗Ln的分解。我们将这些结果与Johnson图的Terwilliger代数联系起来。我们用二项式系数来表示Johnson图的Terwilliger代数的维数。

引用次数: 0

A modular approach to Andrews-Beck partition statistics Andrews-Beck分区统计的模块化方法

IF 1.1 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2023-11-15 DOI: 10.1016/j.jcta.2023.105832

Renrong Mao

Andrews recently provided a q-series proof of congruences for $N T (m, k, n)$ , the total number of parts in the partitions of n with rank congruent to m modulo k. Motivated by Andrews' works, Chern obtain congruences for $M_{ω} (m, k, n)$ which denotes the total number of ones in the partition of n with crank congruent to m modulo k. In this paper, we focus on the modular approach to these new partition statistics. Applying the theory of mock modular forms, we establish equalities and identities for $N T (m, 7, n)$ and $M_{ω} (m, 7, n)$ .

Andrews最近给出了n的分区中秩与m模k相等的部分的总数NT(m,k,n)的同余的q级数证明。在Andrews的工作的启发下，Chern得到了m ω(m,k,n)的同余，表示n的分区中曲量与m模k相等的部分的总数。在本文中，我们重点讨论了这些新的分区统计量的模方法。应用拟模形式理论，建立了NT(m,7,n)和m ω(m,7,n)的等式和恒等式。

引用次数: 0

A bivariate Q-polynomial structure for the non-binary Johnson scheme 非二元Johnson格式的二元Q多项式结构

IF 1.1 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2023-10-24 DOI: 10.1016/j.jcta.2023.105829

Nicolas Crampé , Luc Vinet , Meri Zaimi , Xiaohong Zhang

The notion of multivariate P- and Q-polynomial association scheme has been introduced recently, generalizing the well-known univariate case. Numerous examples of such association schemes have already been exhibited. In particular, it has been demonstrated that the non-binary Johnson scheme is a bivariate P-polynomial association scheme. We show here that it is also a bivariate Q-polynomial association scheme for some parameters. This provides, with the P-polynomial structure, the bispectral property (i.e. the recurrence and difference relations) of a family of bivariate orthogonal polynomials made out of univariate Krawtchouk and dual Hahn polynomials. The algebra based on the bispectral operators is also studied together with the subconstituent algebra of this association scheme.

最近引入了多元P和Q多项式关联方案的概念，推广了著名的单变量情况。已经展示了许多这样的关联方案的例子。特别地，已经证明了非二进制Johnson格式是一个二元P-多项式关联格式。我们在这里证明了它也是一些参数的二元Q多项式关联方案。这通过P-多项式结构提供了由单变量Krawtchouk多项式和对偶Hahn多项式组成的一组二变量正交多项式的双谱性质（即递推关系和差分关系）。本文还研究了基于双谱算子的代数，以及该关联方案的子结构代数。

引用次数: 2

Non-expansive matrix number systems with bases similar to certain Jordan blocks 基底类似于某些Jordan块的非扩张矩阵数系统

IF 1.1 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2023-10-19 DOI: 10.1016/j.jcta.2023.105828

Joshua W. Caldwell , Kevin G. Hare , Tomáš Vávra

We study representations of integral vectors in a number system with a matrix base M and vector digits. We focus on the case when M is equal or similar to $J_{n}$ , the Jordan block with eigenvalue 1 and dimension n. If $M = J_{2}$ , we classify all digit sets of size two allowing representation for all of $Z^{2}$ . For $M = J_{n}$ with $n \geq 3$ , we show that a digit set of size three suffice to represent all of $Z^{n}$ . For bases M similar to $J_{n}$ , $n \geq 2$ , we construct a digit set of size n such that all of $Z^{n}$ is represented. The language of words representing the zero vector with $M = J_{2}$ and the digits ${(0, \pm 1)}^{T}$ is shown not to be context-free, but to be recognizable by a Turing machine with logarithmic memory.

我们研究了矩阵基M和向量数字的数字系统中积分向量的表示。我们关注当M等于或类似于Jn的情况，Jn是具有特征值1和维数n的Jordan块。如果M=J2，我们对大小为2的所有数字集进行分类，允许表示所有Z2。对于n≥3的M=Jn，我们证明了大小为3的数字集足以表示所有Zn。对于类似于Jn的碱基M，n≥2，我们构造了一个大小为n的数字集，使得所有的Zn都被表示。表示M=J2的零向量和数字（0，±1）T的单词语言被证明不是上下文无关的，而是可以被具有对数记忆的图灵机识别的。

{"title":"Non-expansive matrix number systems with bases similar to certain Jordan blocks","authors":"Joshua W. Caldwell , Kevin G. Hare , Tomáš Vávra","doi":"10.1016/j.jcta.2023.105828","DOIUrl":"https://doi.org/10.1016/j.jcta.2023.105828","url":null,"abstract":"<div>We study representations of integral vectors in a number system with a matrix base M and vector digits. We focus on the case when M is equal or similar to <math><msub><mrow><mi>J</mi></mrow><mrow><mi>n</mi></mrow></msub></math>, the Jordan block with eigenvalue 1 and dimension n. If <math><mi>M</mi><mo>=</mo><msub><mrow><mi>J</mi></mrow><mrow><mn>2</mn></mrow></msub></math>, we classify all digit sets of size two allowing representation for all of <math><msup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msup></math>. For <math><mi>M</mi><mo>=</mo><msub><mrow><mi>J</mi></mrow><mrow><mi>n</mi></mrow></msub></math> with <math><mi>n</mi><mo>≥</mo><mn>3</mn></math>, we show that a digit set of size three suffice to represent all of <math><msup><mrow><mi>Z</mi></mrow><mrow><mi>n</mi></mrow></msup></math>. For bases M similar to <math><msub><mrow><mi>J</mi></mrow><mrow><mi>n</mi></mrow></msub></math>, <math><mi>n</mi><mo>≥</mo><mn>2</mn></math>, we construct a digit set of size n such that all of <math><msup><mrow><mi>Z</mi></mrow><mrow><mi>n</mi></mrow></msup></math> is represented. The language of words representing the zero vector with <math><mi>M</mi><mo>=</mo><msub><mrow><mi>J</mi></mrow><mrow><mn>2</mn></mrow></msub></math> and the digits <math><msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mo>±</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>T</mi></mrow></msup></math> is shown not to be context-free, but to be recognizable by a Turing machine with logarithmic memory.</div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"202 ","pages":"Article 105828"},"PeriodicalIF":1.1,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50187332","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

On some double Nahm sums of Zagier 关于Zagier的一些二重Nahm和

IF 1.1 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2023-10-11 DOI: 10.1016/j.jcta.2023.105819

Zhineng Cao , Hjalmar Rosengren , Liuquan Wang

Zagier provided eleven conjectural rank two examples for Nahm's problem. All of them have been proved in the literature except for the fifth example, and there is no q-series proof for the tenth example. We prove that the fifth and the tenth examples are in fact equivalent. Then we give a q-series proof for the fifth example, which confirms a recent conjecture of Wang. This also serves as the first q-series proof for the tenth example, whose explicit form was conjectured by Vlasenko and Zwegers in 2011 and whose modularity was proved by Cherednik and Feigin in 2013 via nilpotent double affine Hecke algebras.

Zagier为Nahm的问题提供了十一个推测性的秩二例子。除第五个例子外，所有这些都在文献中得到了证明，第十个例子没有q级数证明。我们证明了第五个和第十个例子实际上是等价的。然后我们给出了第五个例子的q级数证明，证实了王最近的一个猜想。这也是第十个例子的第一个q级数证明，其显式形式由Vlasenko和Zwegers在2011年推测，其模块性由Cherednik和Feigin在2013年通过幂零双仿射Hecke代数证明。

引用次数: 1

Union-closed sets and Horn Boolean functions 并集闭集与Horn布尔函数

IF 1.1 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2023-10-11 DOI: 10.1016/j.jcta.2023.105818

Vadim Lozin , Viktor Zamaraev

A family $F$ of sets is union-closed if the union of any two sets from $F$ belongs to $F$ . The union-closed sets conjecture states that if $F$ is a finite union-closed family of finite sets, then there is an element that belongs to at least half of the sets in $F$ . The conjecture has several equivalent formulations in terms of other combinatorial structures such as lattices and graphs. In its whole generality the conjecture remains wide open, but it was verified for various important classes of lattices, such as lower semimodular lattices, and graphs, such as chordal bipartite graphs. In the present paper we develop a Boolean approach to the conjecture and verify it for several classes of Boolean functions, such as submodular functions and double Horn functions.

一个集合族F是并集闭的，如果来自F的任意两个集合的并集属于F。并集闭集合猜想指出，如果F是有限集合的有限并集闭族，则有一个元素属于F中至少一半的集合。该猜想在其他组合结构（如格和图）方面有几个等价的公式。在其整个一般性中，该猜想仍然是完全开放的，但它已被证明适用于各种重要的格类，如下半模格和图，如弦二分图。在本文中，我们发展了一种布尔猜想的方法，并对几类布尔函数，如子模函数和双Horn函数进行了验证。

引用次数: 0

Cycles of even-odd drop permutations and continued fractions of Genocchi numbers 奇偶数下降排列的循环与Genocchi数的连分式

IF 1.1 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2023-10-01 DOI: 10.1016/j.jcta.2023.105778

Qiongqiong Pan , Jiang Zeng

Recently Lazar and Wachs proved two new permutation models, called D-permutations and E-permutations, for Genocchi and median Genocchi numbers. In a follow-up, Eu et al. studied the even-odd descent permutations, which are in bijection with E-permutations. We generalize Eu et al.'s descent polynomials with eight statistics and obtain an explicit J-fraction formula for their ordinary generaing function. The J-fraction permits us to confirm two conjectures of Lazar-Wachs about cycles of D and E permutations and obtain a $(p, q)$ -analogue of Eu et al.'s gamma-formula. Moreover, the $(p, q)$ gamma-coefficients have the same factorization flavor as the gamma-coefficients of Brändén's $(p, q)$ -Eulerian polynomials.

最近，Lazar和Wachs为Genocchi数和Genocchi中值证明了两个新的排列模型，称为D-排列和E-排列。在后续的研究中，Eu等人研究了奇偶下降排列，它与E-排列是双射的。我们用八个统计量推广了Eu等人的下降多项式，并得到了它们的普通生成函数的一个显式J分数公式。J分数允许我们证实Lazar-Wachs关于D和E置换循环的两个猜想，并获得Eu等人的伽玛公式的（p，q）-类似物。此外，（p，q）伽玛系数与Brändén（p，q）-欧拉多项式的伽玛系数具有相同的因子分解风格。

引用次数: 3

Further investigations on permutation based constructions of bent functions bent函数基于置换构造的进一步研究

IF 1.1 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A

Pub Date : 2023-10-01 DOI: 10.1016/j.jcta.2023.105779

Kangquan Li , Chunlei Li , Tor Helleseth , Longjiang Qu

Constructing bent functions by composing a Boolean function with a permutation was introduced by Hou and Langevin in 1997. The approach appears simple but heavily depends on the construction of desirable permutations. In this paper, we further study this approach by investigating the exponential sums of certain monomials and permutations. We propose several classes of bent functions from quadratic permutations and permutations with (generalized) Niho exponents, and also a class of bent functions from a generalization of the Maiorana-McFarland class. The relations among the proposed bent functions and the known families of bent function are studied. Numerical results show that our constructions include bent functions that are not contained in the completed Maiorana-McFarland class $M^{#}$ , the class ${PS}_{a p}$ or the class $H$ .

1997年，Hou和Langevin提出了用置换组合布尔函数来构造bent函数。该方法看起来很简单，但在很大程度上取决于所需排列的构造。在本文中，我们通过研究某些单项式和置换的指数和来进一步研究这种方法。我们从二次置换和具有（广义）Niho指数的置换中提出了几类bent函数，并从Maiorana-McFarland类的推广中提出了一类bent功能。研究了所提出的bent函数与已知bent函数族之间的关系。数值结果表明，我们的构造包括不包含在已完成的Maiorana-McFarland类M#、类PSap或类H中的bent函数。

引用次数: 0

首页上一页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Journal of Combinatorial Theory Series A

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀