标题： 一种广义的伯日对应关系和$k$-测度的分拆 显示英文标题

标题： A Generalized Burge Correspondence and $k$-measure of Partitions

摘要： 设$P$为整数分拆的集合，$D$为其中具有不同部分的子集。 我们扩展了 Burge 在分拆和二进制字之间的对应关系，以将$D$和$D$编码为在$k$元字母表上的字，对于任何固定的$k\geq 2$。 这些编码被用于证明两个涉及$k$度量的分拆恒等式的细化，这些恒等式最近由 Andrews、Chern 和 Li 通过代数方法推导出来。 我们对$D$的编码与最小间隔大小分拆恒等式（例如 Schur 定理）之间的关系也进行了简要讨论。 显示英文摘要

摘要： Let $P$ be the set of integer partitions and $D$ the subset of those with distinct parts. We extend a correspondence of Burge between partitions and binary words to give encodings of both $D$ and $D$ as words over a $k$-ary alphabet, for any fixed $k\geq 2$. These are used to prove refinements of two partition identities involving $k$-measure that were recently derived algebraically by Andrews, Chern and Li. The relationship between our encoding of $D$ and minimum gap-size partition identities (e.g. Schur's Theorem) is also briefly discussed.