The number of partial Steiner systems and $d$-partitions
Combinatorics
2022-02-21 v4
Abstract
We prove asymptotic upper bounds on the number of -partitions (paving matroids of fixed rank) and partial Steiner systems (sparse paving matroids of fixed rank), using a mixture of entropy counting, sparse encoding, and the probabilistic method.
Keywords
Cite
@article{arxiv.1811.11810,
title = {The number of partial Steiner systems and $d$-partitions},
author = {Remco van der Hofstad and Rudi Pendavingh and Jorn van der Pol},
journal= {arXiv preprint arXiv:1811.11810},
year = {2022}
}
Comments
Journal version; article is now published in Advances in Combinatorics