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Chen","submitted_at":"2012-03-20T01:14:35Z","abstract_excerpt":"For $k\\geq i\\geq 1$, let $B_{k,i}(n)$ denote the number of partitions of $n$ such that part 1 appears at most $i-1$ times, two consecutive integers l and $l+1$ appear at most $k-1$ times and if l and $l+1$ appear exactly $k-1$ times then the total sum of the parts l and $l+1$ is congruent to $i-1$ modulo 2. Let $A_{k,i}(n)$ denote the number of partitions with parts not congruent to $i$, $2k-i$ and $2k$ modulo $2k$. Bressoud's theorem states that $A_{k,i}(n)=B_{k,i}(n)$. 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