Related papers: Supersolvable resolutions of line arrangements
Recently developed supersymmetric perturbation theory has been successfully employed to make a complete mathematical analysis the reason behind exact solvability of some non-central potentials. This investigation clarifies once more the…
It has been shown earlier that the solubility of the Legendre and the associated Legendre equations can be understood as a consequence of an underlying supersymmetry and shape invariance. We have extended this result to the hypergeometric…
This paper mainly focuses on cones whose basis is a maximum $h$-scattered linear set. We start by investigating the intersection sizes of such cones with the hyperplanes. Then we analyze two constructions of point sets with few intersection…
In this work some nonlinear integral equation is studied. This equation has arisen in the (super)string field theory and cosmology. In this work it is proved that some boundary problem for this equation has a solution.
The concept of super solution is a special type of generalized solutions with certain degree of robustness and stability. In this paper we consider the $(1,1)$-super solutions of the model RB. Using the first moment method, we establish a…
Arrangements of lines and pseudolines are fundamental objects in discrete and computational geometry. They also appear in other areas of computer science, such as the study of sorting networks. Let $B_n$ be the number of nonisomorphic…
We prove that under certain combinatorial conditions, the realization spaces of line arrangements on the complex projective plane are connected. We also give several examples of arrangements with eight, nine and ten lines which have…
The SHGH conjecture proposes a solution to the question of how many conditions a general union of fat points imposes on the complete linear system of curves in $\mathbb P^2$ of fixed degree $d$, and it is known to be true in many cases. We…
In this paper we present a new bound obtained with the probabilistic method for the solution of the Set Covering problem with unit costs. The bound is valid for problems of fixed dimension, thus extending previous similar asymptotic…
We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the the order of singularities of the coefficients and provide examples to illustrate the…
In this paper we give constructions for infinite sequences of finite non-linear locally recoverable codes $\mathcal C\subseteq \prod\limits^N_{i=1}\mathbb F_{q_i}$ over a product of finite fields arising from basis expansions in algebraic…
Error bounds have been studied for more than seventy years, beginning with the seminal result of Hoffman (1952) [{\it J. Res. Natl. Bur. Standards}, 49 (1952), 263--265], which establishes an upper bound for the distance from an arbitrary…
A line arrangement of $3n$ lines in $\mathbb CP^2$ satisfies Hirzebruch property if each line intersect others in $n+1$ points. Hirzebruch asked if all such arrangements are related to finite complex reflection groups. We give a positive…
We obtain upper bounds on the composition length of a finite permutation group in terms of the degree and the number of orbits, and analogous bounds for primitive, quasiprimitive and semiprimitive groups. Similarly, we obtain upper bounds…
Wakamiko determined bases and the exponents for multiarrangements of three lines over a field of characteristic zero. In this paper, we study the exponents of multiarrangements of three lines for the case of positive characteristic. We…
We study a new flexible method to extend linearly the graph of a non-linear, and usually not bijective, function so that the resulting extension is a bijection. Our motivation comes from cryptography. Examples from symmetric cryptography…
We study different extended formulations for the set $X = \{x\in\mathbb{Z}^n \mid Ax = Ax^0\}$ in order to tackle the feasibility problem for the set $X_+=X \cap \mathbb{Z}^n_+$. Here the goal is not to find an improved polyhedral…
This work considers special types of interval linear systems - overdetermined systems. Simply said these systems have more equations than variables. The solution set of an interval linear system is a collection of all solutions of all…
We state the formula for the critical number of vertices of a convex lattice polygon that guarantees that the polygon contains at least one point of a given sublattice and give a partial proof of the formula. We show that the proof can be…
We investigate the definability (reducts) lattice of the order of integers and describe a sublattice generated by relations 'between', 'cycle', 'separation', 'neighbor', '1-codirection', 'order' and equality'. Some open questions are…