PartitionMobius

A name from the enumeratio catalogue with no kernel of its own yet; this page carries its crosswalk only.

Mapped through to sage for the oracle; not yet written up here.

PartitionMobius(...)Mapped through to sage for the oracle; not yet written up here.

Typed signatures

Type	Package	Applies
(number, number) -> integer	diagram	always

Domain: Oracle

Plot

Examples

Basic #

$\mu = -1$ on the two-block interval

live ↗

In$\mathrm{PartitionMobius}(\mathrm{Diagram}(\bigl\lbrack\bigl\lbrack1\bigr\rbrack, \bigl\lbrack-1\bigr\rbrack\bigr\rbrack), \mathrm{Diagram}(\bigl\lbrack\bigl\lbrack1, -1\bigr\rbrack\bigr\rbrack))$Out$-1$

$\mu(\hat 0, \hat 1) = (-1)^{k-1}(k-1)!$ for $k = 3$ blocks

live ↗

In$\mathrm{PartitionMobius}(\mathrm{Diagram}(\bigl\lbrack\bigl\lbrack1, -1\bigr\rbrack, \bigl\lbrack2\bigr\rbrack, \bigl\lbrack-2\bigr\rbrack\bigr\rbrack), \mathrm{Diagram}(\bigl\lbrack\bigl\lbrack1, 2, -1, -2\bigr\rbrack\bigr\rbrack))$Out$2$

About

Examples	2
Checked against	SageMath 2 agree
Crosswalk	SageMath

Implementation

mappedsagepackages/oracle/src/mappings.ts

Sage's posets.SetPartitions, on the 2k points relabelled 1…2k: finer below coarser.