Výsledky vyhledávání - "Peter J. Dukes"

An ( n 3 ) configuration is an incidence structure equivalent to a linear hypergraph on n vertices which is both 3-regular and 3-uniform. We investigate a variant in which one constraint, say 3-regularity, is present, and we allow exactly one line to

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::d363109e1082eda78fd754d3ae0fc239
https://doi.org/10.26493/1855-3974.1685.395

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Constructions of Sarvate-Beam Group Divisible Designs

Autor: Peter J. Dukes, Joanna Niezen

A balanced incomplete block design is a set system in which all pairs of distinct elements occur with a constant frequency. By contrast, a Sarvate-Beam design induces an interval of distinct frequencies on pairs. In this paper, we settle the existenc

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Balancing permuted copies of multigraphs and integer matrices

Autor: Coen del Valle, Peter J. Dukes

Given a square matrix $A$ over the integers, we consider the $\mathbb{Z}$-module $M_A$ generated by the set of all matrices that are permutation-similar to $A$. Motivated by analogous problems on signed graph decompositions and block designs, we are

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A lower bound on permutation codes of distance $$n-1$$

Autor: Peter J. Dukes, Sergey Bereg

Publikováno v: Designs, Codes and Cryptography. 88:63-72

A classical recursive construction for mutually orthogonal latin squares (MOLS) is shown to hold more generally for a class of permutation codes of length n and minimum distance $$n-1$$. When such codes of length $$p+1$$ are included as ingredients,

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::289a5101ab62b17ac49cd6b5a4126d3f
https://doi.org/10.1007/s10623-019-00670-5

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Constructions and uses of incomplete pairwise balanced designs

Autor: Esther R. Lamken, Peter J. Dukes

Publikováno v: Designs, Codes and Cryptography. 87:2729-2751

We give explicit constructions for incomplete pairwise balanced designs IPBD((v; w), K), or, equivalently, edge-decompositions of a difference of two cliques $$K_v \setminus K_w$$ into cliques whose sizes belong to the set K. Our constructions produc

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fb44067e4f9d1200b99609034b8ad074
https://doi.org/10.1007/s10623-019-00645-6

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Fractional triangle decompositions of dense $3$-partite graphs

Autor: Flora C. Bowditch, Peter J. Dukes

Publikováno v: Journal of Combinatorics. 10:255-282

We compute a minimum degree threshold sufficient for 3-partite graphs to admit a fractional triangle decomposition. Together with recent work of Barber, K\"uhn, Lo, Osthus and Taylor, this leads to bounds for exact decompositions and in particular th

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::109a01e5ee4bfcdeb34df18242e45704
https://doi.org/10.4310/joc.2019.v10.n2.a5

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A lower bound on HMOLS with equal sized holes

Autor: Michael Bailey, Peter J. Dukes, Coen del Valle

It is known that N ( n ) , the maximum number of mutually orthogonal latin squares of order n, satisfies the lower bound N ( n ) ≥ n 1 / 14.8 for large n. For h ≥ 2 , relatively little is known about the quantity N ( h n ) , which denotes the max

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