arXiv subjects

Jerome Kelleher

Publications and source records attributed to Jerome Kelleher.

3 recordsLinked to original sources

arXiv2026

Population-scale Ancestral Recombination Graphs with tskit 1.0

Ancestral recombination graphs (ARGs) are an increasingly important component of population and statistical genetics. The tskit library has become key infrastructure for the field, providing an expressive and general representation of ARGs together with a suite of efficient fundamental operations. In this note, we announce tskit version 1.0, describe its underlying rationale, and document its stability guarantees. These guarantees provide a foundation for durable computational artefacts and support long-term reproducibility of code and analyses.

q-bio.PE↗

arXiv2014

Generating All Partitions: A Comparison Of Two Encodings

Integer partitions may be encoded as either ascending or descending compositions for the purposes of systematic generation. Many algorithms exist to generate all descending compositions, yet none have previously been published to generate all ascending compositions. We develop three new algorithms to generate all ascending compositions and compare these with descending composition generators from the literature. We analyse the new algorithms and provide new and more precise analyses for the descending composition generators. In each case, the ascending composition generation algorithm is substantially more efficient than its descending composition counterpart. We develop a new formula for the partition function p(n) as part of our analysis of the lexicographic succession rule for ascending compositions.

cs.DS↗

arXiv2010

The large-parts formula for p(n)

A new formula for the partition function $p(n)$ is developed. We show that the number of partitions of $n$ can be expressed as the sum of a simple function of the two largest parts of all partitions. Specifically, if $a_1 + >... + a_k = n$ is a partition of $n$ with $a_1 \leq ... \leq a_k$ and $a_0 = 0$, then the sum of $\lfloor(a_k + a_{k-1}) / (a_{k-1} + 1)\rfloor$ over all partitions of $n$ is equal to $2p(n) - 1$.

math.CO↗