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Mathematics and statistics journals publish papers on the theory and application of mathematics, statistics, and probability. Most mathematics journals have a broad scope that encompasses most mathematical fields. These commonly include logic and foundations, algebra and number theory, analysis (including differential equations, functional analysis and operator theory), geometry, topology, combinatorics, probability and statistics, numerical analysis and computation theory, mathematical physics, etc.

Mathematics and Statistics

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The famous Hadwiger–Nelson problem asks for the minimum number of colors needed to color the points of the Euclidean plane so that no two points unit distance apart are assigned the same color. In this note we consider a variant of the problem in Minkowski metric planes, where the unit circle is a regular polygon of even and at most 22 vertices. We present a simple lattice–sublattice coloring scheme that uses 6 colors, proving that the chromatic number of the Minkowski planes above are at most 6. This result is new for regular polygons having more than 8 vertices.

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Studia Scientiarum Mathematicarum Hungarica
Authors:
Andras Bezdek
,
Haile Gilroy
,
Owen Henderschedt
, and
Alason Lakhani

John Horton Conway stood out from many famous mathematicians for his love of games and puzzles. Among others, he is known for inventing the two-player topological games called Sprouts and Brussels Sprouts. These games start with n spots (n crosses resp.), have simple rules, last for finitely many moves, and the player who makes the last move wins. In the misère versions, the player who makes the last move loses. In this paper, we make Brussels Sprouts colored, preserving the aesthetic interest and balance of the game. In contrast to the original Sprouts, Colored Brussels Sprouts allows mathematical analysis without computer programming and has winning strategies for a large family of the number of spots.

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Given graphs H and F, the generalized Turán number ex(n, H, F) is the largest number of copies of H in n-vertex F-free graphs. Stability refers to the usual phenomenon that if an n-vertex F-free graph G contains almost ex(n, H, F) copies of H, then G is in some sense similar to some extremal graph. We obtain new stability results for generalized Turán problems and derive several new exact results.

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Let T be a tree. The reducible stem of T is the smallest subtree that contains all branch vertices of T. In this paper, we first use a new technique of Gould and Shull [5] to state a new short proof for a result of Kano et al. [10] on the spanning tree with a bounded number of leaves in a claw-free graph. After that, we use a similar idea to prove a sharp sufficient condition for a claw-free graph having a spanning tree whose reducible stem has few leaves.

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Let n ∈ ℕ. An element (x 1, … , xn ) ∈ En is called a norming point of T L n E if x 1 = = x n = 1 and T x 1 , , x n = T , where L n E denotes the space of all continuous symmetric n-linear forms on E. For T L n E , we define

Norm T = x 1 , , x n E n : x 1 , , x n  is a norming of  T .

Norm(T) is called the norming set of T.

Let · 2 be the plane with a certain norm such that the set of the extreme points of its unit ball ext B · 2 = ± W 1 , ± W 2 for some W 1 ± W 2 · 2 .

In this paper, we classify Norm(T) for every T L n · 2 . We also present relations between the norming sets of L n l 2 and L n l 1 2 .

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This article indicates another set-theoretic formula, solely in terms of union and intersection, for the set of the limits of any given sequence (net, in general) in an arbitrary T 1 space; this representation in particular gives a new characterization of a T 1 space.

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We give all solutions of completely multiplicative functions ƒ , g, for which the equation Ag(n + 1) = Bƒ (n) + C holds for every n ∈ ℕ. We also study the equation G(p + 1) = F(p − 1) + D and we prove some results concerning it.

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We consider a graph whose vertices are legally colored using k colors and ask if the graph contains a k-clique. As it turns out this very special type of k-clique problem is in an intimate connection with constructing schedules. The practicality this clique search based construction of schedules is checked by carrying out numerical experiments.

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Assume that Aj , j ∈ {1, … , m} are positive definite matrices of order n. In this paper we prove among others that, if 0 < l In Aj , j ∈ {1, … , m} in the operator order, for some positive constant l, and In is the unity matrix of order n, then

o 1 2 k = 1 m P k 1 P k det 2 A j l I n 1 / 2 2 1 j < k m P j P k det A j + A k l I n 1 / 2 j = 1 m P j det A j 1 / 2 det k = 1 m P k A k 1 / 2 ,

where Pk ≥ 0 for k ϵ {1, …, m} and j = 1 m P j = 1 .

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The evolute of a conic in the pseudo-Euclidean plane is the locus of centers of all its osculating circles. It’s a curve of order six and class four in general case. In this paper we discuss and compute the order and class of evolutes of different types of conics. We will highlight those cases that have no analogy in the Euclidean plane.

Open access