From the 1 of 7 linked papers with an AI index.
7 papers
Submultiplicative Polynomials in Combinatorics
Krystian Gajdzica, Bernhard Heim, Markus Neuhauser +1
The paper defines recursively constructed polynomials from normalized sequences and investigates when they satisfy a submultiplicative inequality similar to the Bessenrodt–Ono ineq…
Connections between certain numbers related to derangements and -permutations
Piotr Miska, BÅażej Å»mija
For non-negative integer parameters define \begin{align*} \cal{D}(r,u,m,n) := \big\{\ Ï\in \cal{S}_{r+n}\ \big|\ Ï(x)=y \textrm{ for exactly } u \textrm{ pairs } (x,y)…
Large gaps between values of several binary quadratic forms
BÅażej Å»mija
In this paper we study the problem of long gaps between values of binary quadratic forms. Let , be negative integers and be th…
Counting polynomials with positive roots
Pavlo Yatsyna, BÅażej Å»mija
This paper investigates the number of monic integer polynomials of degree whose roots are all real and positive. We establish an asymptotic formula for the case of fixed trace…
Bounded ranges of cardinal functions
Jacek Marchwicki, BÅażej Å»mija
Let be a (non-empty) sequence of positive real numbers. Its achievement set is the set of all the possible sums of the elements of .…
Real quadratic fields with a universal quadratic form of given rank have density zero
Vitezslav Kala, Pavlo Yatsyna, BÅażej Å»mija
We prove an explicit upper bound on the number of real quadratic fields that admit a universal quadratic form of a given rank, thus establishing a density zero statement. More gene…