EPISODE · Aug 20, 2025 · 5 MIN
OEIS A000311: Schroeder’s Fourth Problem and the Web of Combinatorics
from Intellectually Curious · host Mike Breault
In this episode we explore OEIS A000311—Schroeder’s fourth problem—counting labeled series-reduced rooted trees with N leaves. We unpack what ‘series-reduced’ means, see how the same numbers pop up in total partitions of N, series-parallel networks with N-labeled edges, and singleton-reduced phylogenetic trees, and glimpse how generating functions reveal a shared structure behind biology, networks, and number theory. Along the way we glimpse the rapid growth and the unity of seemingly different counting problems.Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical information.Sponsored by Embersilk LLC
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In this episode we explore OEIS A000311—Schroeder’s fourth problem—counting labeled series-reduced rooted trees with N leaves. We unpack what ‘series-reduced’ means, see how the same numbers pop up in total partitions of N, series-parallel networks with N-labeled edges, and singleton-reduced phylogenetic trees, and glimpse how generating functions reveal a shared structure behind biology, networks, and number theory. Along the way we glimpse the rapid growth and the unity of seemingly differe...
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OEIS A000311: Schroeder’s Fourth Problem and the Web of Combinatorics
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