Young Diagrams
An alternative visual representation of an integer partition is its Young diagram, named after the British mathematician Alfred Young. Rather than representing a partition with dots, as in the Ferrers diagram, the Young diagram uses boxes. Thus, the Young diagram for the partition 5 + 4 + 1 is
while the Ferrers diagram for the same partition is
While this seemingly trivial variation doesn't appear worthy of separate mention, Young diagrams turn out to be extremely useful in the study of symmetric functions and group representation theory: in particular, filling the boxes of Young diagrams with numbers (or sometimes more complicated objects) obeying various rules leads to a family of objects called Young tableaux, and these tableaux have combinatorial and representation-theoretic significance.
Read more about this topic: Partition (number Theory)
Famous quotes containing the words young and/or diagrams:
“I’m hurt, hurt and humiliated beyond endurance, seeing the wheat ripening, the fountains never ceasing to give water, the sheep bearing hundreds of lambs, the she-dogs, until it seems the whole country rises to show me its tender sleeping young while I feel two hammer-blows here instead of the mouth of my child.”
—Federico García Lorca (1898–1936)
“Professors could silence me then; they had figures, diagrams, maps, books.... I was learning that books and diagrams can be evil things if they deaden the mind of man and make him blind or cynical before subjection of any kind.”
—Agnes Smedley (1890–1950)