equals the number of 0s to the right, which is between index -1 and 0 in the 01-sequence; visually this corresponds to the main diagonal in the Young diagram). Notice the mnemonic “RGB” for the colourings, starting after the ${{\textbf{\Large |}}}$ mark. The grey shapes indicate a sequence of 3-hooks that can be removed from $\lambda$, to finally obtain the 3-core $(3,1)$ of $\lambda$. One could start with the yellow shape for instance, and then make various choices for the order of the removals. The process always ends with the same $3$-core, $(3,1)$ (see Figure \[fig.hooks\]). Quotients will be $\cdots{\textcolor{red}{0}}{\textcolor{red}{1}}{{\textbf{\Large |}}}{\textcolor{red}{1}}{\textcolor{red}{0}}{\textcolor{red}{1}}{\textcolor{red}{1}}{\textcolor{red}{1}}{\textcolor{red}{1}}{\textcolor{red}{1}}\cdots$ (partition $(2)$), $\cdots{\textcolor{darkgreen}{0}}{{\textbf{\Large |}}}{\textcolor{darkgreen}{1}}{\textcolor{darkgreen}{1}}{\textcolor{darkgreen}{1}}{\textcolor{darkgreen}{1}}{\textcolor{darkgreen}{1}}{\textcolor{darkgreen}{1}}{\textcolor{darkgreen}{1}}\cdots$ (empty partition) and $\cdots{\textcolor{blue}{0}}{\textcolor{blue}{1}}{\textcolor{blue}{1}}{{\textbf{\Large |}}}{\textcolor{blue}{0}}{\textcolor{blue}{1}}{\textcolor{blue}{1}}{\textcolor{blue}{1}}{\textcolor{blue}{0}}{\textcolor{blue}{1}}\cdots$ (partition $(5,2)$). Remark that the yellow shape connects two labels in the 01-sequence that are blue. It thereby corresponds to a specific box of the quotient partition $(5,2)$ (see Figure \[fig.hooks\] and compare with Equation ).\[fig.sequence\][]{data-label="fig.01"}](01sequence.png){width="78.00000%"}

Let $p$ be a positive integer, not necessarily prime. We say that a partition $\lambda$ is a *$p$-core* if it has no hook of length divisible by $p$ (it is actually equivalent to ask for the partition not to have a hook of length exactly $p$). For instance, $(3,1)$ is a 3-core as can 