The number of partial Steiner systems and d-partitions

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The number of partial Steiner systems and d-partitions

van der Hofstad, Remco; Pendavingh, Rudy; van der Pol, Jorn

Advances in Combinatorics (Online), 2/2022

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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.

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van der Hofstad, Remco | Pendavingh, Rudy | van der Pol, Jorn

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