2 citations · 4 across the 10 of their papers we have counts for
11 papers
A Moser-spindle-free 5-chromatic unit distance graph on 2131 vertices in the plane
Jan Kristian Haugland
With regard to the Hadwiger-Nelson problem, several 5-chromatic unit distance graphs in the Euclidean plane have been discovered in recent years. While most constructions rely heav…
A lower bound on the number of bent squares
Jan Kristian Haugland
Bent functions are Boolean functions that are maximally nonlinear. They can be represented as bent squares, i.e., square matrices for which each row and each column is the Walsh sp…
On the number of Hamiltonian cycles in the generalized Petersen graph
Jan Kristian Haugland
The generalized Petersen graph is a cubic graph with vertex set and edge set $E(G(n, k)) = \{v_i v_{i+1}…
New classes of reversible cellular automata
Jan Kristian Haugland, Tron Omland
A Boolean function on ~bits induces a shift-invariant vectorial Boolean function from bits to bits for every . If is bijective for every , we say…
On the max min of the algebraic degree and the nonlinearity of a Boolean function on an affine subspace
Jan Kristian Haugland
We investigate the max min of the algebraic degree and the nonlinearity of a Boolean function in variables when restricted to a -dimensional affine subspace of $\mathbb{F}_2…
A generalization of the hexastix arrangement to higher dimensions
Jan Kristian Haugland
Hexastix is an arrangement of non-overlapping infinite hexagonal prisms in four different directions that cover of space. We consider a possible generalization to …
Shift-invariant transformations and almost liftings
Jan Kristian Haugland, Tron Omland
We investigate shift-invariant transformations, also known as rotation-symmetric vectorial Boolean functions, on bits that are induced from Boolean functions on bits, for $…
Regular grid subgraphs of maximal girth
Jan Kristian Haugland
The unit-distance graph on the -dimensional integer lattice is called the -dimensional grid. We attempt to maximize the girth of a -regular (possibly induce…
Largest polyomino with no four cells equally spaced on a straight line
Jan Kristian Haugland
The maximal number of cells in a polyomino with no four cells equally spaced on a straight line is determined to be 142. This is based on several partial results, each of which can…
The minimum overlap problem revisited
Jan Kristian Haugland
For a given partition of (1, 2, ..., 2n) into two disjoint subsets A and B with n elements in each, consider the maximum number of times any integer occurs as the difference betwee…
Evaluating the Fabius function
Jan Kristian Haugland
The Thue-Morse sequence (1, -1, -1, 1, -1, 1, 1, ...) can in a sense be naturally extended to a continuous function f called the Fabius function. It is shown how to determine the e…