# Journal of Combinatorial Designs (J Combin Des )

## Description

The Journal of Combinatorial Designs is an international journal devoted to the timely publication of the most influential papers in the area of combinatorial design theory. All topics in design theory and in which design theory has important applications are covered including: block designs t-designs pairwise balanced designs and group divisible designs Latin squares quasigroups and related algebras computational methods in design theory construction methods applications in computer science experimental design theory and coding theory graph decompositions factorizations and design-theoretic techniques in graph theory and extremal combinatorics finite geometry and its relation with design theory. algebraic aspects of design theory. Researchers and scientists can depend on the Journal of Combinatorial Designs for the most recent developments in this rapidly growing field and to provide a forum for both theoretical research and applications.

- Impact factor0.69
- 5-year impact0.63
- Cited half-life8.20
- Immediacy index0.12
- Eigenfactor0.00
- Article influence0.65
- WebsiteJournal of Combinatorial Designs website
- Other titlesJournal of combinatorial designs (Online), Journal of combinatorial designs
- ISSN1520-6610
- OCLC41616630
- Material typeDocument, Periodical, Internet resource
- Document typeInternet Resource, Computer File, Journal / Magazine / Newspaper

## Publisher details

- Pre-print
- Author can archive a pre-print version

- Post-print
- Author can archive a post-print version

- Conditions
- See Wiley-Blackwell entry for articles after February 2007
- On personal web site or secure external website at authors institution
- Deposit in institutional repositories is not allowed
- JASIST authors may deposit in an institutional repository
- Non-commercial
- Pre-print must be accompanied with set phrase (see individual journal copyright transfer agreements)
- Published source must be acknowledged with set phrase (see individual journal copyright transfer agreements)
- Publisher's version/PDF cannot be used
- Articles in some journals can be made Open Access on payment of additional charge
- 'John Wiley and Sons' is an imprint of 'Wiley'

- Classification green

## Publications in this journal

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**ABSTRACT:**Using the technique of amalgamation-detachment, we show that the complete equipartite multigraph can be decomposed into cycles of lengths (plus a 1-factor if the degree is odd) whenever there exists a decomposition of into cycles of lengths (plus a 1-factor if the degree is odd). In addition, we give sufficient conditions for the existence of some other, related cycle decompositions of the complete equipartite multigraph .Journal of Combinatorial Designs 12/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**Let L be a latin square of indeterminates. We explore the determinant and permanent of L and show that a number of properties of L can be recovered from the polynomials and per(L). For example, it is possible to tell how many transversals L has from per(L), and the number of 2 × 2 latin subsquares in L can be determined from both and per(L). More generally, we can diagnose from or per(L) the lengths of all symbol cycles. These cycle lengths provide a formula for the coefficient of each monomial in and per(L) that involves only two different indeterminates. Latin squares A and B are trisotopic if B can be obtained from A by permuting rows, permuting columns, permuting symbols, and/or transposing. We show that nontrisotopic latin squares with equal permanents and equal determinants exist for all orders that are divisible by 3. We also show that the permanent, together with knowledge of the identity element, distinguishes Cayley tables of finite groups from each other. A similar result for determinants was already known.Journal of Combinatorial Designs 11/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**If a cycle decomposition of a graph G admits two resolutions, and , such that for each resolution class and , then the resolutions and are said to be orthogonal. In this paper, we introduce the notion of an orthogonally resolvable cycle decomposition, which is a cycle decomposition admitting a pair of orthogonal resolutions. An orthogonally resolvable cycle decomposition of a graph G may be represented by a square array in which each cell is either empty or filled with a k–cycle from G, such that every vertex appears exactly once in each row and column of the array and every edge of G appears in exactly one cycle. We focus mainly on orthogonal k-cycle decompositions of and (the complete graph with the edges of a 1-factor removed), denoted . We give general constructions for such decompositions, which we use to construct several infinite families. We find necessary and sufficient conditions for the existence of an OCD(n, 4). In addition, we consider orthogonal cycle decompositions of the lexicographic product of a complete graph or cycle with . Finally, we give some nonexistence results.Journal of Combinatorial Designs 11/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**We introduce the notion of a partial geometric difference family as a variation on the classical difference family and a generalization of partial geometric difference sets. We study the relationship between partial geometric difference families and both partial geometric designs and difference families, and show that partial geometric difference families give rise to partial geometric designs. We construct several infinite families of partial geometric difference families using Galois rings and the cyclotomy of Galois fields. From these partial geometric difference families, we generate a list of infinite families of partial geometric designs and directed strongly regular graphs.Journal of Combinatorial Designs 11/2014; -
##### Article: Sylow Theory for Quasigroups

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**ABSTRACT:**This paper is intended as a first step toward a general Sylow theory for quasigroups and Latin squares. A subset of a quasigroup lies in a nonoverlapping orbit if its respective translates under the elements of the left multiplication group remain disjoint. In the group case, each nonoverlapping orbit contains a subgroup, and Sylow's Theorem guarantees nonoverlapping orbits on subsets whose order is a prime-power divisor of the group order. For the general quasigroup case, the paper investigates the relationship between non-overlapping orbits and structural properties of a quasigroup. Divisors of the order of a finite quasigroup are classified by the behavior of nonoverlapping orbits. In a dual direction, Sylow properties of a subquasigroup P of a finite left quasigroup Q may be defined directly in terms of the homogeneous space , and also in terms of the behavior of the isomorphism type within the so-called Burnside order, a labeled order structure on the full set of all isomorphism types of irreducible permutation representations.Journal of Combinatorial Designs 10/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**Candelabra quadruple systems (CQS) were first introduced by Hanani who used them to determine the existence of Steiner quadruple systems. In this paper, a new method has been developed by constructing partial candelabra quadruple systems with odd group size, which is a generalization of the even cases, to complete a design. New results of candelabra quadruple systems have been obtained, i.e. we show that for any , there exists a CQS for all , and .Journal of Combinatorial Designs 09/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**The notion of a symmetric Hamiltonian cycle system (HCS) of a graph Γ has been introduced and studied by J. Akiyama, M. Kobayashi, and G. Nakamura [J Combin Des 12 (2004), 39–45] for , by R. A. Brualdi and M. W. Schroeder [J Combin Des 19 (2011), 1–15] for , and then naturally extended by V. Chitra and A. Muthusamy [Discussiones Mathematicae Graph Theory, to appear] to the multigraphs and . In each case, there must be an involutory permutation ψ of the vertices fixing all the cycles of the HCS and at most one vertex. Furthermore, for , this ψ should be precisely the permutation switching all pairs of endpoints of the edges of I.An HCS is cyclic if it is invariant under some cyclic permutation of all the vertices. The existence question for a cyclic HCS of has been completely solved by Jordon and Morris [Discrete Math (2008), 2440–2449]—and we note that their cyclic construction is also symmetric for (mod 8). It is then natural to study the existence problem of an HCS of a graph or multigraph Γ as above which is both cyclic and symmetric. In this paper, we completely solve this problem: in the case of even order, the final answer is that cyclicity and symmetry can always cohabit when a cyclic solution exists. On the other hand, imposing that a cyclic HCS of odd order is also symmetric is very restrictive; we prove in fact that an HCS of with both properties exists if and only if is a prime.Journal of Combinatorial Designs 09/2014; 22(9). -
##### Article: Multidimensional Permanents and an Upper Bound on the Number of Transversals in Latin Squares

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**ABSTRACT:**The permanent of a multidimensional matrix is the sum of products of entries over all diagonals. A nonnegative matrix whose every 1-dimensional plane sums to 1 is called polystochastic. A latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and each column. A transversal of such a square is a set of n entries such that no two entries share the same row, column, or symbol. Let T(n) be the maximum number of transversals over all latin squares of order n. Here, we prove that over the set of multidimensional polystochastic matrices of order n the permanent has a local extremum at the uniform matrix for whose every entry is equal to . Also, we obtain an asymptotic value of the maximal permanent for a certain set of nonnegative multidimensional matrices. In particular, we get that the maximal permanent of polystochastic matrices is asymptotically equal to the permanent of the uniform matrix, whence as a corollary we have an upper bound on the number of transversals in latin squaresJournal of Combinatorial Designs 09/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**We provide general criteria for orthogonal arrays and t-designs on equitable partitions of a hypercube by exploring harmonic distributions. Generalized harmonic weight enumerators for real-valued functions of are introduced and applied to eigenfunctions of the adjacency matrix of . Using this, expressions for harmonic distributions are established for every cell of an equitable partition π of . Moreover, for any given cell in the partition π, the strength of the cell as an orthogonal array is explicitly expressed, and also a characterization of a t-design of that cell is established. We also compute strengths of cells and find t-designs from cells based on constructions of Krotov, Borges, Rifa, and Zinoviev.Journal of Combinatorial Designs 09/2014; -
##### Article: The Complete Arcs of PG(2,31)

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**ABSTRACT:**We obtained a full computer classification of all complete arcs in the Desarguesian projective plane of order 31 using essentially the same methods as for earlier results for planes of smaller order, i.e., isomorph-free backtracking using canonical augmentation. We tabulate the resulting numbers of complete arcs according to size and automorphism group. We give explicit descriptions for all complete arcs with an automorphism group of size at least 20. In some of these cases the constructions can be generalized to other values of q. In particular, we find arcs of size 20 for any field of order , and a complete 44-arc in PG(2,67) with an automorphism group of order 88. We also correct a result by Kéri : there are 12 complete 22-arcs in PG(2,31) up to projective equivalence, and not 11.Journal of Combinatorial Designs 09/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**Given five positive integers and t where and a t-general covering design is a pair where X is a set of n elements (called points) and a multiset of k-subsets of X (called blocks) such that every p-subset of X intersects at least λ blocks of in at least t points. In this article we continue the work carried out by Etzion, Wei, and Zhang [Des. Codes Cryptogr. 5 (1995), 217–239] on the asymptotic covering density of general covering designs. We will present combinatorial constructions leading to new upper bounds on the asymptotic covering density of 4-(n, 4, 6, 1) general covering designs and 4- general covering designs with . The new bound on the asymptotic covering density of 4-(n, 4, 6, 1) general covering designs is equivalent to a new lower bound for the Turán density .Journal of Combinatorial Designs 09/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**Symmetric orthogonal arrays and mixed orthogonal arrays are useful in the design of various experiments. They are also a fundamental tool in the construction of various combinatorial configurations. In this paper, we investigated the mixed orthogonal arrays with four and five factors of strength two, and proved that the necessary conditions of such mixed orthogonal arrays are also sufficient with several exceptions and one possible exception.Journal of Combinatorial Designs 08/2014; 22(8). - [Show abstract] [Hide abstract]

**ABSTRACT:**A -semiframe of type is a -GDD of type , , in which the collection of blocks can be written as a disjoint union where is partitioned into parallel classes of and is partitioned into holey parallel classes, each holey parallel class being a partition of for some . A -SF is a -semiframe of type in which there are p parallel classes in and d holey parallel classes with respect to . In this paper, we shall show that there exists a (3, 1)-SF for any if and only if , , , and .Journal of Combinatorial Designs 08/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**Latin hypercube designs have been found very useful for designing computer experiments. In recent years, several methods of constructing orthogonal Latin hypercube designs have been proposed in the literature. In this article, we report some more results on the construction of orthogonal Latin hypercubes which result in several new designs.Journal of Combinatorial Designs 08/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**2-(v,k,1) designs admitting a primitive rank 3 automorphism group , where G0 belongs to the Extraspecial Class, or to the Exceptional Class of Liebeck's Theorem in [23], are classified.Journal of Combinatorial Designs 08/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**A G-design of order n is a decomposition of the complete graph on n vertices into edge-disjoint subgraphs isomorphic to G. Grooming uniform all-to-all traffic in optical ring networks with grooming ratio C requires the determination of graph decompositions of the complete graph on n vertices into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The existence spectrum problem of G-designs for five-vertex graphs is a long standing problem posed by Bermond, Huang, Rosa and Sotteau in 1980, which is closely related to traffic groomings in optical networks. Although considerable progress has been made over the past 30 years, the existence problems for such G-designs and their related traffic groomings in optical networks are far from complete. In this paper, we first give a complete solution to this spectrum problem for five-vertex graphs by eliminating all the undetermined possible exceptions. Then, we determine almost completely the minimum drop cost of 8-groomings for all orders n by reducing the 37 possible exceptions to 8. Finally, we show the minimum possible drop cost of 9-groomings for all orders n is realizable with 14 exceptions and 12 possible exceptions.Journal of Combinatorial Designs 07/2014; -
##### Article: Classification of Graeco-Latin Cubes

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**ABSTRACT:**A q-ary code of length n, size M, and minimum distance d is called an code. An code with is said to be maximum distance separable (MDS). Here one-error-correcting () MDS codes are classified for small alphabets. In particular, it is shown that there are unique (5, 53, 3)5 and (5, 73, 3)7 codes and equivalence classes of (5, 83, 3)8 codes. The codes are equivalent to certain pairs of mutually orthogonal Latin cubes of order q, called Graeco-Latin cubes.Journal of Combinatorial Designs 06/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**A 1-factorization of a graph G is a decomposition of G into edge-disjoint 1-factors (perfect matchings), and a perfect 1-factorization is a 1-factorization in which the union of any two of the 1-factors is a Hamilton cycle. We consider the problem of the existence of perfect 1-factorizations of even order 4-regular Cayley graphs, with a particular interest in circulant graphs. In this paper, we study a new family of graphs, denoted , which are Cayley graphs if and only if k is even or . By solving the perfect 1-factorization problem for a large class of graphs, we obtain a new class of 4-regular bipartite circulant graphs that do not have a perfect 1-factorization, answering a problem posed in [7]. With further study of graphs, we prove the nonexistence of P1Fs in a class of 4-regular non-bipartite circulant graphs, which is further support for a conjecture made in [7].Journal of Combinatorial Designs 06/2014;

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