The number of partial Steiner systems and d-partitions

The number of partial Steiner systems and d-partitions

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.

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Veröffentlicht in:Advances in Combinatorics (Online) 2022-02
Hauptverfasser: van der Hofstad, Remco, Pendavingh, Rudy, van der Pol, Jorn
Format: Artikel
Sprache:eng
Online-Zugang:Volltext
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Zusammenfassung: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.
ISSN:2517-5599
2517-5599
DOI:10.19086/aic.32563