LargestMultiplicity

The largest multiplicity of a part.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000904via IntegerComposition✓↗St001933via IntegerPartition✓↗

LargestMultiplicity(partition)The largest multiplicity of a part.

Typed signatures

Type	Package	Applies
(composition | integer_partition) -> number	combinatorics	always

Domain: Partition statistics

Details

• Defined over IntegerPartition as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
• Takes a IntegerPartition and nothing else — it reads values against their positions, or walks the orbits, so it needs the bijection. Applying it to a bare list is a type error, not a wrong answer.

Definition

Epsil, as the implementation runs it.

on IntegerPartition, over _x

0 if Length(_x) < 1 else Max(Map(
                                  Function(
                                            Count(Filter(
                                                          Range(1, Length(_x)),
                                                          Function(
                                                                    _x[i] == k,
                                                                    i,
                                                                  ),
                                                        )),
                                            k,
                                          ),
                                  Range(1, Max(_x)),
                                ))

on IntegerComposition, over _x

0 if Length(_x) < 1 else Max(Map(
                                  Function(
                                            Count(Filter(
                                                          Range(1, Length(_x)),
                                                          Function(_x[j] ==
                                                                   _x[i], j),
                                                        )),
                                            i,
                                          ),
                                  Range(1, Length(_x)),
                                ))

Examples

Basic #

the partition $4 + 2 + 1$ of $7$

live ↗

In$\mathrm{LargestMultiplicity}({\operatorname{IntegerPartition}}([4, 2, 1]))$Out$1$

the partition $3 + 3 + 1$ of $7$

live ↗

In$\mathrm{LargestMultiplicity}({\operatorname{IntegerPartition}}([3, 3, 1]))$Out$2$

Properties #

FindStat's value for [1]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([1]), \text{LargestMultiplicity})$Out$1$

Known value · FindStat St001933

FindStat's value for [2]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([2]), \text{LargestMultiplicity})$Out$1$

Known value · FindStat St001933

FindStat's value for [3]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerPartition}}([3]), \text{LargestMultiplicity})$Out$1$

Known value · FindStat St001933

About

Examples	5
Crosswalk	FindStat ×2