A Bijection for Partitions with All Ranks at Least t Extended
نویسندگان
چکیده
It follows from work of Andrews and Bressoud that for t the number of partitions of n with all successive ranks at least t is equal to the number of partitions of n with no part of size t However no simple combinatorial explanation of this fact has appeared in the literature We give a simple bijection for this identity which generalizes a result of Cheema and Gordon for rowed plane partitions The bijection yields several re nements of the identity when the partition counts are parametrized by the minimum successive rank the number of parts and or the size of the Durfee rectangle In addition it gives a natural interpretation of the di erence of shifted successive Gaussian polynomials which we relate to other interpretations of Andrews and Fishel
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A Bijection for Partitions with All Ranks at Least tSylvie
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