相关论文: Expansions in multiple bases over general alphabet…
Using methods developed by Coons and Tyler, we give a new proof of a recent result of Defant, by determining the maximal order of the number of hyper-($b$-ary)-expansions of a nonnegative integer $n$ for general integral bases $b\geqslant…
Given a primitive collection of vectors in the integer lattice, we count the number of ways it can be extended to a basis by vectors with sup-norm bounded by $T$, producing an asymptotic estimate as $T \to \infty$. This problem can be…
We present an algebraic structure in modules over integer rings with cardinality prime powers, which allows to define bases. With such structure, we prove a similar version for the basis extension theorem of linear algebra over fields.…
We introduce and study series expansions of real numbers with an arbitrary Cantor real base $\boldsymbol{\beta}=(\beta_n)_{n\in\mathbb{N}}$, which we call $\boldsymbol{\beta}$-representations. In doing so, we generalize both representations…
In this paper, we present Sch\"utzenberger's factorization in different combinatorial contexts and show that its validity is not restricted to these cases but can be extended to every Lie algebra endowed with an ordered basis. We also…
The partial sums of integer sequences that count the occurrences of a specific pattern in the binary expansion of positive integers have been investigated by different authors since the 1950s. In this note, we introduce generalized pattern…
Binary field extensions are fundamental to many applications, such as multivariate public key cryptography, code-based cryptography, and error-correcting codes. Their implementation requires a foundation in number theory and algebraic…
Factor systems are a tool for working on the extension problem of algebraic structures such as groups, Lie algebras, and associative algebras. Their applications are numerous and well-known in these common settings. We construct…
We introduce and study expansions of real numbers with respect to two integer bases.
We examine the following version of a classic combinatorial search problem introduced by R\'enyi: Given a finite set $X$ of $n$ elements we want to identify an unknown subset $Y \subset X$ of exactly $d$ elements by testing, by as few as…
In this paper, we attempt to develop the Schreier theory for two special types extensions of multiplicative Lie algebras.
In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…
Experiences with the implementation of strong Gr\"obner bases respectively standard bases for polynomial rings over principal ideal rings are explained: different strategies for creating the pair set, methods to avoid coefficient growth and…
We develop a framework for nonstandard analysis that gives foundations to the interplay between external and internal iterations of the star map, and we present a few examples to show the strength and flexibility of such a nonstandard…
This work is devoted to the investigation of the problem about inverse mapping systems expansions of ultrauniform spaces $X$ using polyhedra over non-Archimedean locally compact fields $\bf L$. Theorems about expansions of complete…
In this work, we generalize the integer enumeration basis. We also construct bijections between the elements of special sets and the elements of some groups, and treat the special case of the hyperoctohedral groups. Then, we find a code…
The branching coefficients in the expansion of the elementary symmetric function multiplied by a symmetric Macdonald polynomial $P_\kappa(z)$ are known explicitly. These formulas generalise the known $r=1$ case of the Pieri-type formulas…
We study the Cantor real base numeration system which is a common generalization of two positional systems, namely the Cantor system with a sequence of integer bases and the R\'enyi system with one real base. We focus on the so-called…
This contribution is devoted to the study of positional numeration systems with negative base introduced by Ito and Sadahiro in 2009, called (-\beta)-expansions. We give an admissibility criterion for more general case of…
We extend Paley-Wiener results in the Bargmann setting deduced earlier by the author together with E. Nabizadeh and C. Pfeuffer to larger class of power series expansions. At the same time we deduce characterisations of all Pilipovi{\'c}…