Joshua E. Ducey

activity

20102023

most citedThe Elementary Divisors of the Incidence Matrix of Skew Lines in PG(3,q)

4 citations · 9 across the 6 of their papers we have counts for

collaborators

11 papers

math.CO2023

Integer diagonal forms for subset intersection relations

Joshua E. Ducey, Lauren Engelthaler, Jacob Gathje +3

For integers $0 \leq ℓ \leq k_{r} \leq k_{c} \leq n$ , we give a description for the Smith group of the incidence matrix with rows (columns) indexed by the size $k_{r}$ ( $k_{c}$ , res…

math.CO2022★ 2 cited

A representation-theoretic computation of the rank of $1$ -intersection incidence matrices: $2$ -subsets vs. $n$ -subsets

Joshua E. Ducey, Colby J. Sherwood

Let $W_{k, n}^{i} (m)$ denote a matrix with rows and columns indexed by the $k$ -subsets and $n$ -subsets, respectively, of an $m$ -element set. The row $S$ , column $T$ entry of $W_{k,n…

math.CO2019

Critical group structure from the parameters of a strongly regular graph

Joshua E. Ducey, David L. Duncan, Wesley J. Engelbrecht +4

We give simple arithmetic conditions that force the Sylow $p$ -subgroup of the critical group of a strongly regular graph to take a specific form. These conditions depend only on th…

math.CO2017

The critical group of the Kneser graph on $2$ -subsets of an $n$ -element set

Joshua E. Ducey, Ian Hill, Peter Sin

In this paper we compute the critical group of the Kneser graph $K G (n, 2)$ . This is equivalent to computing the Smith normal form of a Laplacian matrix of this graph.

math.CO2017★ 3 cited

The Smith group and the critical group of the Grassmann graph of lines in finite projective space and of its complement

Joshua E. Ducey, Peter Sin

We compute the elementary divisors of the adjacency and Laplacian matrices of the Grassmann graph on $2$ -dimensional subspaces in a finite vector space. We also compute the corresp…

math.CO2015

On the critical group of the missing Moore graph

Joshua E. Ducey

We consider the critical group of a hypothetical Moore graph of diameter $2$ and valency $57$ . Determining this group is equivalent to finding the Smith normal form of the Laplacia…

math.CO2015

The Smith and Critical Groups of the Square Rook's Graph and its Complement

Joshua E. Ducey, Jonathan Gerhard, Noah Watson

Let $R_{n}$ denote the graph with vertex set consisting of the squares of an $n \times n$ grid, with two squares of the grid adjacent when they lie in the same row or column. This…

math.CO2013

Integer invariants of abelian Cayley graphs

Joshua E. Ducey, Deelan M. Jalil

Let $G$ be a finite abelian group, let $E$ be a subset of $G$ , and form the Cayley (directed) graph of $G$ with connecting set $E$ . We explain how, for various matrices associated…

math.CO2013

Integer invariants of an incidence matrix related to Rota's basis conjecture

Stephanie Bittner, Joshua Ducey, Xuyi Guo +2

We compute the spectrum and Smith normal form of the incidence matrix of disjoint transversals, a combinatorial object closely related to the n-dimensional case of Rota's basis con…

math.CO2011★ 4 cited

The Elementary Divisors of the Incidence Matrix of Skew Lines in PG(3,q)

Andries E. Brouwer, Joshua E. Ducey, Peter Sin

The elementary divisors of the incidence matrix of lines in PG(3,q) are computed, where two lines are incident if and only if they are skew.

math.CO2010

The Elementary Divisors of the Incidence Matrices of Skew Lines in PG(3,p)

Joshua Ducey, Peter Sin

The elementary divisors of the incidence matrices of lines in $P G (3, p)$ are computed, where two lines are incident if and only if they are skew.