Multiplication theorems for self-conjugate partitions

In 2011, Han and Ji proved addition-multiplication theorems for integer partitions, from which they derived modular analogues of many classical identities involving hook-length. the present paper, we prove subset self-conjugate partitions. Although difficulties arise due to parity questions, are almost always able include BG-rank introduced by Berkovich Garvan. This gives us as consequences versions hook-lengths Our tools mainly based on fine properties Littlewood decomposition restricted partitions.Mathematics Subject Classifications: 05A15, 05A17, 05A19, 05E05, 05E10, 11P81Keywords: Hook-length formulas, BGP-ranks, Integers decomposition, core partitions