Reconstruction of Partitions

Abstract

For the partition $x=[x_1\ge x_2\ge \cdots\ge x_k]$ of the integer $n=\sum_{i}\, x_{i}$ a $t$-deletion is a partition $y=[y_1\ge y_2\ge \cdots\ge y_k]$ with $x_{i}\geq y_{i}\geq 0$ and $\sum_{i}\, (x_{i}-y_{i})=t$. We prove that all partitions of $n$ are reconstructible from their $t$–deletions if $n$ is sufficiently large in relation to $t$.