Upper Bounds on Integer Partitions
Stichworte:
combinatorics, number theory, sum-rank metric
combinatorics, number theory, sum-rank metric
Beschreibung
How many ways are there to write down n nonnegative integers, all of which being strictly smaller than q, such that their sum is k? In other words, what is the coefficient of x^k in (1 + x + ... + x^(q-1))^n?
In this thesis, we are going to dive into the integer partitioning problem with a certain number of partitions and an upper bound on partition size.
The goal of this thesis is to take an already existing bound for the value mentioned above, which holds for a specific k value - and extend it to general k.
The upper bound can then be used for proving better upper bounds in coding theory for certain metrics other than the Hamming metric.
[1] H. B.-S. Couvée, T. Jerkovits, and J. Bariffi, ‘Bounds on Sphere Sizes in the Sum-Rank Metric and Coordinate-Additive Metrics’, Des. Codes Cryptogr., Mar. 2025, doi: 10.1007/s10623-025-01604-0.
Voraussetzungen
information theory, channel coding, strong interest in combinatorics and number theory
Betreuer:
Gökberk Erdogan,Hugo Sauerbier Couvée