Combinatorial Trades: A Survey of Recent Results

Billington, Elizabeth J.

doi:10.1007/978-1-4613-0245-2_3

Cited by 23 publications

(22 citation statements)

References 18 publications

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“…If the entries are real (hence ±1) the matrix is Hadamard. The notion of a trade is well known in the study of t-designs and Latin squares [1]. For a complex Hadamard matrix we define a trade to be a set of entries which can be altered to obtain a different complex Hadamard matrix of the same order.…”

Section: Introductionmentioning

confidence: 99%

Trades in Complex Hadamard Matrices

Catháin

Wanless

2015

Springer Proceedings in Mathematics &Amp; Statistics

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A trade in a complex Hadamard matrix is a set of entries which can be changed to obtain a different complex Hadamard matrix. We show that in a real Hadamard matrix of order n all trades contain at least n entries. We call a trade rectangular if it consists of a submatrix that can be multiplied by some scalar c = 1 to obtain another complex Hadamard matrix. We give a characterisation of rectangular trades in complex Hadamard matrices of order n and show that they all contain at least n entries. We conjecture that all trades in complex Hadamard matrices contain at least n entries.

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Section: Introductionmentioning

confidence: 99%

Trades in Complex Hadamard Matrices

Catháin

Wanless

2015

Springer Proceedings in Mathematics &Amp; Statistics

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“…We call such a G-trade a graphical trade to distinguish it from trades based on other combinatorial objects, such as blocks designs and Latin squares. The various forms of combinatorial trades are surveyed in [8,1].…”

Section: Introductionmentioning

confidence: 99%

The volume and foundation of star trades

Lefevre

2008

Discrete Mathematics

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An x-star trade consists of two disjoint decompositions of some simple graph H into copies of K 1,x , the graph known as the x-star. The number of vertices of H is referred to as the foundation of the trade, while the number of copies of K 1,x in each of the decompositions is called the volume of the trade. We determine all values of x, v and s for which there exists a K 1,x -trade of volume s and foundation v.

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“…The concept of a combinatorial trade was first formally applied in design theory in the 1960s (see Hedayat [8]), although the idea was used much earlier (see [11] and [2] for a full survey of work in trades).…”

Section: Introductionmentioning

confidence: 99%

Steiner trade spectra of complete partite graphs

Lefevre

2004

Discrete Mathematics

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The Steiner trade spectrum of a simple graph G is the set of all integers t for which there is a simple graph H whose edges can be partitioned into t copies of G in two entirely different ways. The Steiner trade spectra of complete partite graphs were determined in all but a few cases in a recent paper by Billington and Hoffman (Discrete Math. 250 (2002) 23). In this paper we resolve the remaining cases.

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Combinatorial Trades: A Survey of Recent Results

Cited by 23 publications

References 18 publications

Trades in Complex Hadamard Matrices

Trades in Complex Hadamard Matrices

The volume and foundation of star trades

Steiner trade spectra of complete partite graphs

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