Self-Conjugate Partitions Dimension And It's Incidence Matrix.

The conjugate partition is similar to a transpose of a matrix; we switch the rows with columns, or the index of a part with the part itself. Self-conjugate partitions are partitions that are equal to their conjugate; previously, the only known way to verify whether a partition is self-conjugate was through the use of a Young diagram. In this paper we will illustrate the dimension of self conjugate partition. Also we will illustrate a matrix for conjugate partition graph. Theorems and examples will be discussed.