EPISODE · Jun 27, 2025 · 13 MIN
OEIS A000262: Partitions of sets into ordered lists
from Intellectually Curious · host Mike Breault
A000262 counts the number of ways to partition an n-element set into any number of nonempty ordered lists (an unordered collection of ordered blocks). We’ll trace the definition through small n (1, 1, 3, 13, 73, …) and then dive into the surprising connections: the same numbers arise from multiplying cycle lengths over all permutations, from Walsh’s chain gangs, and from Navarrete’s circular-table representations with a chosen representative from each group. We’ll also glimpse its d-finite nature, recurrence structure, and the broader web of combinatorial interpretations that tie these ideas together.Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical information.Sponsored by Embersilk LLC
Embed this episode
What this episode covers
A000262 counts the number of ways to partition an n-element set into any number of nonempty ordered lists (an unordered collection of ordered blocks). We’ll trace the definition through small n (1, 1, 3, 13, 73, …) and then dive into the surprising connections: the same numbers arise from multiplying cycle lengths over all permutations, from Walsh’s chain gangs, and from Navarrete’s circular-table representations with a chosen representative from each group. We’ll also glimpse its d-finite na...
NOW PLAYING
OEIS A000262: Partitions of sets into ordered lists
No transcript for this episode yet
Similar Episodes
No similar episodes found.
Similar Podcasts
No similar podcasts found.