Durfee square

In number theory, a Durfee square is an attribute of an integer partition. A partition of n has a Durfee square of size s if s is the largest number such that the partition contains at least s parts with values ≥ s.^[1] An equivalent, but more visual, definition is that the Durfee square is the largest square that is contained within a partition's Ferrers diagram.^[2] The side-length of the Durfee square is known as the rank of the partition.^[3]

The Durfee symbol consists of the two partitions represented by the points to the right or below the Durfee square.

^ Andrews, George E.; Eriksson, Kimmo (2004). Integer Partitions. Cambridge University Press. p. 76. ISBN 0-521-60090-1.
^ Canfield, E. Rodney; Corteel, Sylvie; Savage, Carla D. (1998). "Durfee polynomials". Electronic Journal of Combinatorics. 5. Research Paper 32. doi:10.37236/1370. MR 1631751.
^ Stanley, Richard P. (1999) Enumerative Combinatorics, Volume 2, p. 289. Cambridge University Press. ISBN 0-521-56069-1.

[1] Andrews, George E.; Eriksson, Kimmo (2004). Integer Partitions. Cambridge University Press. p. 76. ISBN 0-521-60090-1.

[2] Canfield, E. Rodney; Corteel, Sylvie; Savage, Carla D. (1998). "Durfee polynomials". Electronic Journal of Combinatorics. 5. Research Paper 32. doi:10.37236/1370. MR 1631751.

[3] Stanley, Richard P. (1999) Enumerative Combinatorics, Volume 2, p. 289. Cambridge University Press. ISBN 0-521-56069-1.

[1]

[2]

[3]