Zobrazeno 1 - 10
of 40
pro vyhledávání: '"Cathain, Padraig O"'
Centraliser algebras of monomial representations of finite groups may be constructed and studied using methods similar to those employed in the study of permutation groups. Guided by results of D. G. Higman and others, we give an explicit constructio
Externí odkaz:
http://arxiv.org/abs/2409.14352
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