Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Congruences for Fishburn numbers modulo prime powers
View through CrossRef
The Fishburn numbers ξ(n) are defined by the formal power series [Formula: see text] Recently, Andrews and Sellers discovered congruences of the form ξ(pm + j) ≡ 0 modulo p, valid for all m ≥ 0. These congruences have then been complemented and generalized to the case of r-Fishburn numbers by Garvan. In this note, we answer a question of Andrews and Sellers regarding an extension of these congruences to the case of prime powers. We show that, under a certain condition, all these congruences indeed extend to hold modulo prime powers.
Title: Congruences for Fishburn numbers modulo prime powers
Description:
The Fishburn numbers ξ(n) are defined by the formal power series [Formula: see text] Recently, Andrews and Sellers discovered congruences of the form ξ(pm + j) ≡ 0 modulo p, valid for all m ≥ 0.
These congruences have then been complemented and generalized to the case of r-Fishburn numbers by Garvan.
In this note, we answer a question of Andrews and Sellers regarding an extension of these congruences to the case of prime powers.
We show that, under a certain condition, all these congruences indeed extend to hold modulo prime powers.
Related Results
Infinite families of congruences modulo $2$ for $(\ell, k)$-regular partitions
Infinite families of congruences modulo $2$ for $(\ell, k)$-regular partitions
Let $b_{\ell, k}(n)$ denote the number of $(\ell, k)$-regular partition of $n$. Recently, some congruences modulo $2$ for $ (3, 8), (4, 7)$-regular partition and modulo $8$, modul...
Teaching Congruences in Connection with Diophantine Equations
Teaching Congruences in Connection with Diophantine Equations
The presented paper is devoted to the new teaching model of congruences of computer science students within the subject of discrete mathematics at universities. The main goal was t...
Interactive Visualization of Line Congruences for Spatial Mechanism Design
Interactive Visualization of Line Congruences for Spatial Mechanism Design
This paper presents a framework for generating, representing, and interacting with the line congruences associated with four general finite poses. These line congruences are the so...
Prime Numbers Calculation Formulas
Prime Numbers Calculation Formulas
The application of prime numbers in modern science, especially in computer
science, is very wide. Since prime numbers can only divisible by 1 and themselves,
they are not factored ...
Congruences for hook lengths of partitions
Congruences for hook lengths of partitions
Recently, Amdeberhan
et al.
[Proc. Amer. Math. Soc. Ser. B 11 (2024), pp. 345–357] proved congruences for the number of hooks of fixed even ...
SEPARATION OF POWERS IN THE RUSSIAN SYSTEM OF FISCAL FEDERALISM
SEPARATION OF POWERS IN THE RUSSIAN SYSTEM OF FISCAL FEDERALISM
The aim of the research is to identify the main trends in separation of powers of the Russian Federation and subjects of the Russian Federation in the context of the new federal la...
The Canberra Bubble
The Canberra Bubble
According to the ABC television program Four Corners, “Parliament House in Canberra is a hotbed of political intrigue and high tension … . It’s known as the ‘Canberra Bubble’ and i...
Računalno potpomognuto usmjeravanje kod dvojezičnih govornika
Računalno potpomognuto usmjeravanje kod dvojezičnih govornika
This thesis investigates whether modern computer models can confirm how people encounter words and then use these findings in didactics. In recent years, computers have been used i...