LegOfFirstCell

The leg of cell (1,1): the number of parts minus one.

LegOfFirstCell(partition)The leg of cell (1,1): the number of parts minus one.

Typed signatures

Type	Package	Applies
(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 Map(Function(Count(Filter(
                                                    Range(1, Length(_x)),
                                                    Function(_x[j] >= i, j),
                                                  )), i), Range(1, Max(_x)))[1] -
                         1

Examples

Basic #

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

live ↗

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

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

live ↗

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

About

Examples	2