Number theory MOC

Numeric partition

A partition of a number 𝑛 βˆˆβ„•0 is just a set of numbers adding to 𝑛. num In order to have uniqueness, a partition is defined as an infinite sequence (πœ†π‘–)βˆžπ‘–=1 in β„•0 that adds to 𝑛 and is non-increasing.

  1. πœ†π‘– β‰₯πœ†π‘–+1 for all 𝑖 βˆˆβ„•
  2. βˆ‘π‘›π‘–=1πœ†π‘– =𝑛

A graphical portrayal of a partition is a Young diagram.

Ordering

Partitions can be ordered by

  • πœ† =πœ‡ iff πœ†π‘– =πœ‡π‘– for all 𝑖 βˆˆβ„•
  • πœ† >πœ‡ iff the first non-vanishing πœ†π‘– βˆ’πœ‡π‘– is positive

tidy | en | SemBr

Graph View

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