Journal of Combinatorial Designs最新文献

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3-Designs From PSL ( 2 , q ) With Cyclic Starter Blocks 从PSL （2, q）的设计与循环起动块

IF 0.8 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs

Pub Date : 2025-11-02 DOI: 10.1002/jcd.22014

Akihide Hanaki, Kenji Kobayashi, Akihiro Munemasa

<div> We consider when the projective special linear group over a finite field defines a block-transitive 3-design with a starter block which is a multiplicative subgroup of the field. For a prime power <math> <semantics> <mrow> <mrow> <mi>q</mi> <mo>≡</mo> <mn>1</mn> <mspace></mspace> <mrow> <mo>(</mo> <mrow> <mi>mod</mi> <mspace></mspace> <mn>20</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mrow> </semantics></math>, we will show that the multiplicative subgroup of order 5 is a starter block of a 3-design if and only if the multiplicative subgroup of order 10 is a starter block of a 3-design. The former is the family of 3-<math> <semantics> <mrow> <mrow> <mrow> <mo>(</mo> <mrow> <mi>q</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>3</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mrow> </semantics></math> designs investigated by Li, Deng and Zhang, while the latter appear in a different context by Bonnecaze and Solé for the case <math> <semantics> <mrow> <mrow> <mi>q</mi> <mo>=</mo> <mn>41</mn> </mrow> </mrow> </semantics></math>. We also show a similar equivalence for multiplicative subgroups of orders 13 and 26 for a prime power <math> <semantics> <mrow> <mrow> <mi>q</mi> <mo>≡</mo> <mn>1</mn> <mspace></mspace> <mrow>

考虑有限域上的射影特殊线性群定义了具有域的乘子群为起始块的块传递3-设计。对于素数幂q≡1 （mod 20）)，我们将证明，当且仅当10阶乘法子群是3阶设计的起始块时，5阶乘法子群是3阶设计的起始块。前者是3- (q + 1,5，3)李、邓、张调查的设计；而后者则出现在Bonnecaze和sol针对q = 41的不同语境中。对于素数幂q≡1 (mod . 1)，我们也给出了类似的13阶和26阶乘法子群的等价性52)。

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引用次数: 0

Binary Codes From Subset Inclusion Matrices 子集包含矩阵的二进制码

IF 0.8 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs

Pub Date : 2025-10-12 DOI: 10.1002/jcd.22012

Alexey D. Marin, Ivan Yu. Mogilnykh

In this paper, we study the minimum distances of binary linear codes with parity check matrices formed from subset inclusion matrices $� � � � � �_{W � � � t � �, � � n � �, � � k � �} � � �$ , representing $� � � � � t � � �$ -element subsets versus $� � � � � k � � �$ -element subsets of an $� � � � � n � � �$ -element set. We provide both lower and upper bounds on the minimum distances of these codes and determine the exact values for any $� � � � � t � � \leq � � 3 � � �$ and sufficiently large $� � � � � n � � �$ . Our study combines design and integer linear programming techniques. The codes we consider are connected to LDPC codes and combinatorial designs. Furthermore, we construct quasi-cyclic LDPC codes from inclusion matrices that exhibit performance comparable to or slightly better than MacKay-type codes when evaluated using bit flipping and min-sum algorithms.

本文研究了由子集包含矩阵W t， n，k ,表示一个n元素集合的t元素子集和k元素子集。我们给出了这些码的最小距离的下界和上界，并确定了任意t≤3和足够大的n的精确值。我们的研究结合了设计和整数线性规划技术。我们所考虑的代码是连接到LDPC代码和组合设计。此外，我们从包含矩阵构建了准循环LDPC码，当使用位翻转和最小和算法进行评估时，其性能与mackay型码相当或略好。

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引用次数: 0

Block-Transitive Automorphism Groups of 2- ( v , 5 , λ ) Designs 2- (v, 5, λ)设计的块传递自同构群

IF 0.8 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs

Pub Date : 2025-10-09 DOI: 10.1002/jcd.22010

Chuhan Lei, Xiaoqin Zhan

<div> This paper investigates 2-<math> <semantics> <mrow> <mrow> <mrow> <mo>(</mo> <mrow> <mi>v</mi> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mi>λ</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mrow> </semantics></math> designs <math> <semantics> <mrow> <mrow> <mi>D</mi> </mrow> </mrow> </semantics></math> admitting a block-transitive automorphism group <math> <semantics> <mrow> <mrow> <mi>G</mi> </mrow> </mrow> </semantics></math>. We first prove that if <math> <semantics> <mrow> <mrow> <mi>G</mi> </mrow> </mrow> </semantics></math> is point-imprimitive, then <math> <semantics> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> </semantics></math> must be one of 16, 21, or 81. We further provide a complete classification of all such designs for <math> <semantics> <mrow> <mrow> <mi>v</mi> <mo>=</mo> <mn>16</mn> </mrow> </mrow> </semantics></math> and <math> <semantics> <mrow> <mrow> <mn>21</mn> </mrow> </mrow> </semantics></math>. Second, we demonstrate that if <math> <semantics> <mrow> <mrow> <mi>G</mi> </mrow> </mrow> </semantics></math> is point-primitive, then it must be of affine type, almost simple type, or product type. Additionally, we present a classification of pairs <math> <semantics> <mrow> <mrow> <mrow>

本文研究了2- (v, 5，λ)设计D承认一个块传递自同构群G。我们首先证明如果G是点非基的，那么v一定是16、21或81中的一个。我们进一步为v = 16和21提供了所有这些设计的完整分类。其次，我们证明了如果G是点基元，那么它一定是仿射型、几乎简单型或积型。此外，我们提出了对的分类(D，G)，其中G为产品类型。

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引用次数: 0

On the Q -Polynomial Property of Bipartite Graphs Admitting a Uniform Structure 具有一致结构的二部图的Q -多项式性质

IF 0.8 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs

Pub Date : 2025-10-09 DOI: 10.1002/jcd.22011

Blas Fernández, Roghayeh Maleki, Štefko Miklavič, Giusy Monzillo

Let <math> <semantics> <mrow> <mrow> <mi>Γ</mi> </mrow> </mrow> </semantics></math> denote a finite, connected graph with vertex set <math> <semantics> <mrow> <mrow> <mi>X</mi> </mrow> </mrow> </semantics></math>. Fix <math> <semantics> <mrow> <mrow> <mi>x</mi> <mo>∈</mo> <mi>X</mi> </mrow> </mrow> </semantics></math> and let <math> <semantics> <mrow> <mrow> <mi>ε</mi> <mo>≥</mo> <mn>3</mn> </mrow> </mrow> </semantics></math> denote the eccentricity of <math> <semantics> <mrow> <mrow> <mi>x</mi> </mrow> </mrow> </semantics></math>. For mutually distinct scalars <math> <semantics> <mrow> <mrow> <msubsup> <mrow> <mo>{</mo> <msubsup> <mi>θ</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mo>}</mo> </mrow> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>ε</mi> </msubsup> </mrow> </mrow> </semantics></math> define a diagonal matrix <math> <semantics> <mrow> <mrow> <msup> <mi>A</mi> <mo>

设Γ表示一个顶点集X的有限连通图。固定x∈x，令ε≥3表示x的偏心率。设Γ表示一个顶点集X的有限连通图。固定x∈x，令ε≥3表示x的偏心率。对于互异标量{θ i *} I = 0 ε定义对角矩阵A * = A * (θ 0 *，θ 1 *，…，θ ε *)∈MatX (R)如下：对于y∈X，令(A *) y y

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引用次数: 0

New Difference Triangle Sets by a Field-Programmable Gate Array-Based Search Technique 基于现场可编程门阵列搜索技术的新差分三角集

IF 0.8 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs

Pub Date : 2025-10-02 DOI: 10.1002/jcd.22009

Mohannad Shehadeh, William Kingsford, Frank R. Kschischang

We provide some difference triangle sets with scopes that improve upon the best known values. These are found with purpose-built digital circuits realized with field-programmable gate arrays (FPGAs) rather than software algorithms running on general-purpose processors.

我们提供了一些差分三角形集，它们的作用域在已知值的基础上得到了改进。这些都是用现场可编程门阵列（fpga）实现的专用数字电路，而不是在通用处理器上运行的软件算法。

引用次数: 0

Completing Multi-Latin Rectangles via Factors With Prescribed Degrees in Bipartite Graphs 用二部图中规定度数的因子补全多拉丁矩形

IF 0.8 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs

Pub Date : 2025-09-28 DOI: 10.1002/jcd.22008

Amin Bahmanian

Let $� � � � � Q � � �$ be an $� � � � � n � � \times � � n � � �$ array whose top left $� � � � � r � � \times � � s � � �$ sub-array $� � � � � L � � �$ is filled with a set of $� � � � � k � � �$ different symbols such that each cell of $� � � � � L � � �$ contains $� � � � � λ � � �$ symbols. In this note, we find conditions under which each empty cell of $� � � � � Q � � �$ can be filled with $� � � � � λ � � �$ symbols in such a way that the total number of occurrences of each symbol is prescribed and that each symbol occurs at most $� � � � � λ � �$

设Q是一个n × n的数组，它的左上角r × s的子数组L被k的集合填充不同的符号，使得L的每个单元格包含λ符号。在这篇文章中，我们找到了可以用λ符号填充Q的每个空单元格的条件，在这样的条件下，每个符号出现的总次数是规定的，并且每个符号出现在在Q的每一行和每一列中。为了证明这一结果，我们建立了一个二部图的子图具有给定度条件的新准则。我们的证明是独立的，依赖于交变路径技术。

{"title":"Completing Multi-Latin Rectangles via Factors With Prescribed Degrees in Bipartite Graphs","authors":"Amin Bahmanian","doi":"10.1002/jcd.22008","DOIUrl":"https://doi.org/10.1002/jcd.22008","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>Q</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> be an <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>×</mo>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> array whose top left <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 \u0000 <mo>×</mo>\u0000 \u0000 <mi>s</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> sub-array <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is filled with a set of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> different symbols such that each cell of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> contains <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>λ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> symbols. In this note, we find conditions under which each empty cell of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>Q</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> can be filled with <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>λ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> symbols in such a way that the total number of occurrences of each symbol is prescribed and that each symbol occurs at most <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>λ</mi>\u0000 </mrow>\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 1","pages":"31-36"},"PeriodicalIF":0.8,"publicationDate":"2025-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.22008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145533770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Variations on Bollobás Systems of d -Partitions d -Partitions的Bollobás系统的变体

IF 0.8 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs

Pub Date : 2025-09-24 DOI: 10.1002/jcd.22007

Yu Fang, Xiaomiao Wang, Tao Feng

This paper investigates five kinds of systems of

� � � d � �

-partitions of

� � � � [�                     � n �                     �] � � �

, including symmetric Bollobás systems, strong Bollobás systems, Bollobás systems, skew Bollobás systems, and weak Bollobás systems. Many known results on variations of Bollobás systems are unified. Especially, we give a negative answer to a conjecture on Bollobás systems of

� � � d � �

-partitions of

� � � � [�                     � n �                     �] � � �

that was presented by Hegedüs and Frankl (European J. Comb., 120 [2024], 103983). Even though this conjecture does not hold for general Bollobás systems, we show that it holds for strong Bollobás systems of

� � � d � �

-partitions of

� � � � [�                     � n �                     �] � � �

本文研究了[n]的五种d -分区系统，包括对称Bollobás系统、强Bollobás系统、Bollobás系统、倾斜Bollobás系统和弱Bollobás系统。许多已知的关于Bollobás系统变化的结果是统一的。特别是，我们对heged和Frankl （European J. Comb）提出的关于[n]的d分区Bollobás系统的猜想给出了否定的答案。科学通报，20 (1)[2024]；尽管这个猜想并不适用于一般的Bollobás系统，但我们证明它适用于[n]的d分区的强Bollobás系统。

{"title":"Variations on Bollobás Systems of \u0000 \u0000 \u0000 d\u0000 \u0000 -Partitions","authors":"Yu Fang, Xiaomiao Wang, Tao Feng","doi":"10.1002/jcd.22007","DOIUrl":"https://doi.org/10.1002/jcd.22007","url":null,"abstract":"<div>\u0000 \u0000 This paper investigates five kinds of systems of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 </semantics></math>-partitions of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>]</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, including symmetric Bollobás systems, strong Bollobás systems, Bollobás systems, skew Bollobás systems, and weak Bollobás systems. Many known results on variations of Bollobás systems are unified. Especially, we give a negative answer to a conjecture on Bollobás systems of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 </semantics></math>-partitions of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>]</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> that was presented by Hegedüs and Frankl (European J. Comb., 120 [2024], 103983). Even though this conjecture does not hold for general Bollobás systems, we show that it holds for strong Bollobás systems of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 </semantics></math>-partitions of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>]</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>.\u0000 </div>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 1","pages":"15-30"},"PeriodicalIF":0.8,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145533702","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}

引用次数: 0

Steiner Triple Systems With High Discrepancy 高差异斯坦纳三系

IF 0.8 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs

Pub Date : 2025-09-09 DOI: 10.1002/jcd.22004

Lior Gishboliner, Stefan Glock, Amedeo Sgueglia

In this paper, we initiate the study of discrepancy questions for combinatorial designs. Specifically, we show that, for every fixed <math> <semantics> <mrow> <mrow> <mi>r</mi> <mo>≥</mo> <mn>3</mn> </mrow> </mrow> </semantics></math> and <math> <semantics> <mrow> <mrow> <mi>n</mi> <mo>≡</mo> <mn>1</mn> <mo>,</mo> <mn>3</mn> <mspace></mspace> <mrow> <mo>(</mo> <mrow> <mi>mod</mi> <mspace></mspace> <mn>6</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mrow> </semantics></math>, any <math> <semantics> <mrow> <mrow> <mi>r</mi> </mrow> </mrow> </semantics></math>-colouring of the triples on <math> <semantics> <mrow> <mrow> <mrow> <mo>[</mo> <mi>n</mi> <mo>]</mo> </mrow> </mrow> </mrow> </semantics></math> admits a Steiner triple system of order <math> <semantics> <mrow> <mrow> <mi>n</mi> </mrow> </mrow> </semantics></math> with discrepancy <math> <semantics> <mrow> <mrow> <mi>Ω</mi> <mrow> <mo>(</mo> <msup> <mi>n</mi> <mn>2</mn> </msup>

本文对组合设计中的差异问题进行了初步研究。具体来说，我们表明，对于每一个固定的r≥3且n≡1,3 (mod 6)；[n]上三元组的任意r着色承认有偏差Ω (n)的n阶斯坦纳三重系统2)。这是不正确的r = 2，但我们能够渐近表征所有的2-着色，不包含一个斯坦纳三重系统与高差异。在我们的证明中，关键的一步是刻画了3-均匀超图，避免了某些自然类型的诱导子图，从而为超图的结构理论做出了贡献。

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引用次数: 0

Maximum Shattering 最大破碎

IF 0.8 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs

Pub Date : 2025-08-29 DOI: 10.1002/jcd.22005

Noga Alon, Varun Sivashankar, Daniel G. Zhu

A family <math> <semantics> <mrow> <mrow> <mi>ℱ</mi> </mrow> </mrow> </semantics></math> of subsets of <math> <semantics> <mrow> <mrow> <mrow> <mo>[</mo> <mi>n</mi> <mo>]</mo> </mrow> <mo>=</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> </mrow> <mo>}</mo> </mrow> </mrow> </mrow> </semantics></math> shatters a set <math> <semantics> <mrow> <mrow> <mi>A</mi> <mo>⊆</mo> <mrow> <mo>[</mo> <mi>n</mi> <mo>]</mo> </mrow> </mrow> </mrow> </semantics></math> if for every <math> <semantics> <mrow> <mrow> <msup> <mi>A</mi> <mo>′</mo> </msup> <mo>⊆</mo> <mi>A</mi> </mrow> </mrow> </semantics></math>, there is an <math> <semantics> <mrow> <mrow> <mi>F</mi> <mo>∈</mo> <mi>ℱ</mi> </mrow> </mrow> </semant

[n] =的子集的一族_{1,2，…，n}粉碎一组a哉[n]如果对每个A ` `,存在一个F∈F∩A= a '。我们开发了一个框架来分析f （n, k）D)；大小为d的[n]的子集的最大可能数目这可能会被一个k人的家庭所打破。在其他结果中，我们确定f (n, k，D)正好满足D≤2的条件如果d和n增大，当d和n - d都趋于无穷时，对于任意满足2d≤k的k≤(1 + 0d)；我们有f （n, k）D) = （1 + 0）(1) cN d，其中c大致为0。 289，是一个大的方阵在f2上可逆的概率。后一个结果扩展了Das和Mészáros的工作。作为一个应用，我们改进了覆盖数组在特定字母大小下存在的边界。

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引用次数: 0

Completing Partial k -Star Designs 完成部分k星设计

IF 0.8 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs

Pub Date : 2025-08-17 DOI: 10.1002/jcd.22003

Ajani De Vas Gunasekara, Daniel Horsley

A $� � � � � k � � �$ -star is a complete bipartite graph $� � � � � �_{K � � � 1 � �, � � k � �} � � �$ . A partial $� � � � � k � � �$ -star design of order $� � � � � n � � �$ is a pair $� � � � � � (� � � V � �, � � A � � �) � � � �$ where $� � � � � V � � �$ is a set of $� � � � � n � � �$ vertices and $� � � � � A � � �$ is a set of edge-disjoint $� � � �$

k *是一个完全二部图k1，k .n阶的部分k星设计是一对(V ,A)其中V是n的集合A是边不相交的k个星的集合，这些星的顶点集是V .如果顶点集V的完全图的每条边都在A中的某个星点上，然后(V)；A)是一个（完全的）k星设计。我们说(V)A)是可完成的，如果有一个k星设计(v)；例：A：在本文中，我们确定，对于所有k和n，n阶不完全部分k星设计中的最小星数。

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引用次数: 0

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Journal of Combinatorial Designs

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