Zobrazeno 1 - 10
of 52
pro vyhledávání: '"Catháin, Padraig Ó"'
Autor:
Devillers, Alice, Kamčev, Nina, McKay, Brendan, Catháin, Padraig Ó, Royle, Gordon, Van de Voorde, Geertrui, Wanless, Ian, Wood, David R.
There are finitely many graphs with diameter $2$ and girth 5. What if the girth 5 assumption is relaxed? Apart from stars, are there finitely many triangle-free graphs with diameter $2$ and no $K_{2,3}$ subgraph? This question is related to the exist
Externí odkaz:
http://arxiv.org/abs/2406.00246
Motivated by an Erd\H{o}s--Ko--Rado type problem on sets of strongly orthogonal roots in the $A_{\ell}$ root system, we estimate bounds for the size of a family of pairs $(A_{i}, B_{i})$ of $k$-subsets in $\{ 1, 2, \ldots, n\}$ such that $A_{i} \cap
Externí odkaz:
http://arxiv.org/abs/2404.04867
The study of regular incidence structures such as projective planes and symmetric block designs is a well established topic in discrete mathematics. Work of Bruck, Ryser and Chowla in the mid-twentieth century applied the Hasse-Minkowski local-global
Externí odkaz:
http://arxiv.org/abs/2308.06008
Segre's theorem on ovals in projective spaces is an ingenious result from the mid-twentieth century which requires surprisingly little background to prove. This note, suitable for undergraduates with experience of linear and abstract algebra, provide
Externí odkaz:
http://arxiv.org/abs/2301.05171
Autor:
Horsley, Daniel, Catháin, Padraig Ó
Publikováno v:
Des. Codes Cryptogr. 90 (2022) 2375-2383
A partial $(n,k,t)_\lambda$-system is a pair $(X,\mathcal{B})$ where $X$ is an $n$-set of vertices and $\mathcal{B}$ is a collection of $k$-subsets of $X$ called blocks such that each $t$-set of vertices is a subset of at most $\lambda$ blocks. A seq
Externí odkaz:
http://arxiv.org/abs/2111.00858
In a celebrated paper of 1893, Hadamard established the maximal determinant theorem, which establishes an upper bound on the determinant of a matrix with complex entries of norm at most $1$. His paper concludes with the suggestion that mathematicians
Externí odkaz:
http://arxiv.org/abs/2104.06756
Quaternary unit Hadamard (QUH) matrices were introduced by Fender, Kharagani and Suda along with a method to construct them at prime power orders. We present a novel construction of real Hadamard matrices from QUH matrices. Our construction recovers
Externí odkaz:
http://arxiv.org/abs/1907.07024
Autor:
Heikoop, Phillip, Catháin, Padraig Ó
For $n \geq 225$ we show that every integer of the form $n + 2m$ such that $0 \leq 2m \leq n^{2} - \frac{9}{2} n \sqrt{n}$ is the dimension of a connected semi-simple subalgebra of $\mathrm{M}_{n}(k)$, that is, a subalgebra isomorphic to a direct sum
Externí odkaz:
http://arxiv.org/abs/1905.03878
Cocyclic Hadamard matrices (CHMs) were introduced by de Launey and Horadam as a class of Hadamard matrices with interesting algebraic properties. \'O Cath\'ain and R\"oder described a classification algorithm for CHMs of order $4n$ based on relative
Externí odkaz:
http://arxiv.org/abs/1904.11460
Autor:
Cathain, Padraig O, Swartz, Eric
Publikováno v:
Discrete Mathematics, 2019, 342, 12, Article 111606
An $n \times n$ matrix $H$ is Butson-Hadamard if its entries are $k^{\text{th}}$ roots of unity and it satisfies $HH^* = nI_n$. Write $BH(n, k)$ for the set of such matrices. Suppose that $k = p^{\alpha}q^{\beta}$ where $p$ and $q$ are primes and $\a
Externí odkaz:
http://arxiv.org/abs/1904.10771