A partition whose conjugate partition is equivalent to itself. The Ferrers diagrams corresponding to the self-conjugate partitions for 3<=n<=10 are illustrated ...

10 авг. 2022 г. · Self-conjugate partitions are partitions that are equal to their conjugate; previously, the only known way to verify whether a partition is self ...

22 дек. 2019 г. · Consider A1 to be the set of all partitions of n into distinct odd parts, and let A2 be the set of all partitions of n into self conjugate ... combinatorics - self-conjugate partitions - Math Stack Exchange For each integer $n > 2$ determine a self-conjugate partition of ... Другие результаты с сайта math.stackexchange.com

10 авг. 2022 г. · Self-conjugate partitions are partitions that are equal to their conjugate; previously, the only known way to verify whether a partition is self ...

30 окт. 2021 г. · The number of self-conjugate partitions of a positive integer n. (1.1) is equal to the number of partitions of n into distinct odd parts. The ...

Here we study SC, the set of all self-conjugate partitions. For a given partition λ, a cell at (i, j) in the Young diagram of λ is the box in the ith-row.

A partition λ is called self-conjugate if λ∗ = λ. This means its Ferrers diagram is symmetric, as in for example λ = (5,5,3,2,2):

We say that an integer partition λ is self-conjugate if λ is the same as its transpose λT obtained by reflecting the Ferrers diagram of λ about the main di-.

In this paper, we prove that self-conjugate -core partitions are equinumerous with symmetric -Dyck paths, confirming a conjecture posed by Cho, Huh and Sohn.