66 citations · 448 across the 34 of their papers we have counts for
17 papers · 1 filter
On hyperovals in
Dmitrii V. Pasechnik
According to a computer search conducted by the author and described in [7], in there are two types of hyperovals, having 72 and 96 points, respectively. Here we give g…
Implementing Hadamard Matrices in SageMath
Matteo Cati, Dmitrii V. Pasechnik
Hadamard matrices are square matrices with mutually orthogonal rows. The Hadamard conjecture states that Hadamard matrices of order exist whenever is , , o…
Random Chain Complexes
Viktor L. Ginzburg, Dmitrii V. Pasechnik
We study random, finite-dimensional, ungraded chain complexes over a finite field and show that for a uniformly distributed differential a complex has the smallest possible homolog…
Implementing Brouwer's database of strongly regular graphs
Nathann Cohen, Dmitrii V. Pasechnik
Andries Brouwer maintains a public database of existence results for strongly regular graphs on vertices. We implemented most of the infinite families of graphs listed…
Edge-dominating cycles, k-walks and Hamilton prisms in -free graphs
Gao Mou, Dmitrii Pasechnik
We show that an edge-dominating cycle in a -free graph can be found in polynomial time; this implies that every 1/(k-1)-tough -free graph admits a k-walk, and it can be…
Sandpile groups of generalized de Bruijn and Kautz graphs and circulant matrices over finite fields
Swee Hong Chan, Henk D. L. Hollmann, Dmitrii V. Pasechnik
A maximal minor of the Laplacian of an -vertex Eulerian digraph gives rise to a finite group known as the sandpile (or critical) gro…
Critical groups of generalized de Bruijn and Kautz graphs and circulant matrices over finite fields: an extended abstract
Swee Hong Chan, Henk D. L. Hollmann, Dmitrii V. Pasechnik
We determine the critical groups of the generalized de Bruijn graphs DB and generalized Kautz graphs Kautz, thus extending and completing earlier results for the clas…
Book drawings of complete bipartite graphs
Etienne de Klerk, Dmitrii V. Pasechnik, Gelasio Salazar
A "book" with k pages consists of a straight line (the "spine") and k half-planes (the "pages"), such that the boundary of each page is the spine. If a graph is drawn on a book wit…
Computing symmetry groups of polyhedra
David Bremner, Mathieu Dutour Sikiric, Dmitrii V. Pasechnik +2
Knowing the symmetries of a polyhedron can be very useful for the analysis of its structure as well as for practical polyhedral computations. In this note, we study symmetry groups…
Improved lower bounds on book crossing numbers of complete graphs
Etienne de Klerk, Dmitrii V. Pasechnik, Gelasio Salazar
A "book with k pages" consists of a straight line (the "spine") and k half-planes (the "pages"), such that the boundary of each page is the spine. If a graph is drawn on a book wit…
Improved lower bounds for the 2-page crossing numbers of K_{m,n} and K_n via semidefinite programming
Etienne de Klerk, Dmitrii V. Pasechnik
It has been long conjectured that the crossing numbers of the complete bipartite graph K_{m,n} and of the complete graph K_n equal Z(m,n) (the value conjectured by Zarankiewicz, wh…
Two distance-regular graphs
Andries E. Brouwer, Dmitrii V. Pasechnik
We construct two families of distance-regular graphs, namely the subgraph of the dual polar graph of type B_3(q) induced on the vertices far from a fixed point, and the subgraph of…
Algebraic Combinatorics in Mathematical Chemistry. Methods and Algorithms. II. Program Implementation of the Weisfeiler-Leman Algorithm
Luitpold Babel, Irina V. Chuvaeva, Mikhail Klin +1
The stabilization algorithm of Weisfeiler and Leman has as an input any square matrix A of order n and returns the minimal cellular (coherent) algebra W(A) which includes A. In cas…
A note on the stability number of an orthogonality graph
E. de Klerk, D. V. Pasechnik
We consider the orthogonality graph Omega(n) with 2^n vertices corresponding to the 0-1 n-vectors, two vertices adjacent if and only if the Hamming distance between them is n/2. We…
Improved bounds for the crossing numbers of K_m,n and K_n
E. de Klerk, J. Maharry, D. V. Pasechnik +2
It has been long--conjectured that the crossing number cr(K_m,n) of the complete bipartite graph K_m,n equals the Zarankiewicz Number Z(m,n):= floor((m-1)/2) floor(m/2) floor((n-1)…
On equicut graphs
Michel Deza, Dmitrii V. Pasechnik
The size sz(G) of an l_1-graph G=(V,E) is the minimum of n_f/t_f over all its possible l_1-embeddings f into n_f-dimensional hypercube with scale t_f. In terms of v=|V|, the sum of…
Bipartite sandwiches: bounding the size of a maximum biclique
Dmitrii V. Pasechnik
Paper withdrawn, due a crucial error in the proof of Lemma 4.3: thus Theorems 1.2 and 1.3 remain unproven.