Related papers: Minimum Critical Exponents for Palindromes

In the present paper, we study extreme negative dependence focussing on the concordance order for copulas. With the absence of a least element for dimensions $d\ge$ 3, the set of all minimal elements in the collection of all copulas turns…

We introduce and study minimal (with respect to inclusion) solutions of systems of tropical linear differential equations. We describe the set of all minimal solutions for a single equation. It is shown that any tropical linear differential…

We show the finiteness of log pluricanonical representations under the assumption of the existence of a good minimal model.

This survey paper discusses five equivalent ways of defining a ``critical point at infinity'' for a complex polynomial of two variables.

Natural numbers satisfying a certain unusual property are defined by the author in a previous note. Later, the author called such numbers $v$-palindromic numbers and proved a periodic phenomenon pertaining to such numbers and repeated…

Using three examples of sequences over a finite alphabet, we want to draw attention to the fact that these sequences having the minimum critical exponent in a given class of sequences show a large degree of symmetry, i.e., they are G-rich…

We give an exponential lower bound for Berge-Ramsey problems.

It is proven that, in any given base, there are infinitely many palindromic numbers having at most six prime divisors, each relatively large. The work involves equidistribution estimates for the palindromes in residue classes to large…

We determine the minimal non-trivial integer group determinant for the dicyclic group of order $4n$ when $n$ is odd. We also discuss the set of all integer group determinants for the dicyclic groups of order $4p$.

Let p be a maximal palindrome in a Sturmian word s=ul_1pl_2v so that p is a palindrome and l_1pl_2 is not for letters l_1 and l_2. Let {\alpha}(p,p') be a morphism mapping letters a and b respectively to a^pb and a^p'b, |p-p'|=1. In this…

The prefix palindromic length $PPL_u(n)$ of an infinite word $u$ is the minimal number of concatenated palindromes needed to express the prefix of length $n$ of $u$. In a 2013 paper with Puzynina and Zamboni we stated the conjecture that…

We study aperiodic balanced sequences over finite alphabets. A sequence vv of this type is fully characterised by a Sturmian sequence u and two constant gap sequences y and y'. We show that the language of v is eventually dendric and we…

We study a new generalization of palindromes and gapped palindromes called block palindromes. A block palindrome is a string that becomes a palindrome when identical substrings are replaced with a distinct character. We investigate several…

We determine the groups of minimal order in which all groups of order n can embedded for 1 < n < 16. We further determine the order of a minimal group in which all groups or order n or less can be embedded, also for 1 < n < 16.

A two-dimensional ($2$D) word is a $2$D palindrome if it is equal to its reverse and it is an HV-palindrome if all its columns and rows are $1$D palindromes. We study some combinatorial and structural properties of HV-palindromes and its…

The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is…

This paper studies the hierarchy of local minimums of a polynomial in the space. For this purpose, we first compute H-minimums, for which the first and second order optimality conditions are satisfied. To compute each H-minimum, we…

For a given $x$ we consider the minimum of $\sum_{n\le x} \chi(n)/n$ as $\chi$ ranges over all quadratic Dirichlet characters. For all large $x$, this minimum is negative and we give upper and lower bounds for it.

We discuss critical elliptic systems in potential form. We prove existence, multiplicity, and compactness of solutions.

In this work we determine the critical exponent for a weakly coupled system of semilinear wave equations with distinct scale-invariant lower order terms, when these terms make both equations in some sense parabolic-like. For the blow-up…