The number of partial Steiner systems and $d$-partitions
Advances in Combinatorics (2022)
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We prove asymptotic upper bounds on the number of $d$-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.
@article{ADVC_2022_a7,
author = {Remco van der Hofstad and Rudi Pendavingh and Jorn van der Pol},
title = {The number of partial {Steiner} systems and $d$-partitions},
journal = {Advances in Combinatorics},
year = {2022},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ADVC_2022_a7/}
}
Remco van der Hofstad; Rudi Pendavingh; Jorn van der Pol. The number of partial Steiner systems and $d$-partitions. Advances in Combinatorics (2022). http://geodesic.mathdoc.fr/item/ADVC_2022_a7/