Zobrazeno 1 - 10
of 102
pro vyhledávání: '"Dukes, Peter P."'
Autor:
Dukes, Peter, Penner, Georgia
The balancing index of a polynomial $f \in \mathbb{Z}[x_1,\dots,x_n]$ is the least positive sum of coefficients in an integer linear combination of permuted copies of $f$ which produces a symmetric polynomial. Here we consider the restricted problem
Externí odkaz:
http://arxiv.org/abs/2408.07679
Autor:
Dukes, Peter J., Lamken, Esther R.
A Steiner triple system, STS$(v)$, is a family of $3$-subsets (blocks) of a set of $v$ elements such that any two elements occur together in precisely one block. A collection of triples consisting of two copies of each block of an STS is called a dup
Externí odkaz:
http://arxiv.org/abs/2406.15614
Autor:
Dukes, Peter J., Nimegeers, Kate
We study a system of linear equations associated with Sudoku latin squares. The coefficient matrix $M$ of the normal system has various symmetries arising from Sudoku. From this, we find the eigenvalues and eigenvectors of $M$, and compute a generali
Externí odkaz:
http://arxiv.org/abs/2310.15279
Publikováno v:
Discrete Analysis, 2024:8, 26 pp
A sequence $\pi_1,\pi_2,\dots$ of permutations is said to be "quasirandom" if the induced density of every permutation $\sigma$ in $\pi_n$ converges to $1/|\sigma|!$ as $n\to\infty$. We prove that $\pi_1,\pi_2,\dots$ is quasirandom if and only if the
Externí odkaz:
http://arxiv.org/abs/2303.04776
For $r\geq1$, the $r$-neighbour bootstrap process in a graph $G$ starts with a set of infected vertices and, in each time step, every vertex with at least $r$ infected neighbours becomes infected. The initial infection percolates if every vertex of $
Externí odkaz:
http://arxiv.org/abs/2209.07594
Autor:
Dukes, Peter J, Gaede, Tao
Given a family $\mathcal{F}=\{A_1,\dots,A_s\}$ of subsets of $\mathbb{Z}_n$, define $\Delta \mathcal{F}$ to be the multiset of all (cyclic) distances dist$(x,y)$, where $\{x,y\} \subset A_i$, $x \neq y$, for some $i=1,\dots,s$. Taking inspiration fro
Externí odkaz:
http://arxiv.org/abs/2208.05527
Autor:
del Valle, Coen, Dukes, Peter J.
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
Externí odkaz:
http://arxiv.org/abs/2201.00897
Autor:
Dukes, Peter J., Niezen, Joanna
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
Externí odkaz:
http://arxiv.org/abs/2201.00865
Autor:
Dukes, Peter, Lamken, Esther
A Kirkman triple system of order $v$, KTS$(v)$, is a resolvable Steiner triple system on $v$ elements. In this paper, we investigate an open problem posed by Doug Stinson, namely the existence of KTS$(v)$ which contain as a subdesign a Steiner triple
Externí odkaz:
http://arxiv.org/abs/2110.07874
Autor:
Dukes, Peter, Niezen, Joanna
We settle the existence of certain "anti-magic" cubes using combinatorial block designs and graph decompositions to align a handful of small examples.
Externí odkaz:
http://arxiv.org/abs/2106.12306