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The -core partitions and the rational Motzkin paths
In this paper, we propose an -abacus for -core
partitions and establish a bijection between the -core
partitions and the rational Motzkin paths of type . This result not
only gives a lattice path interpretation of the -core
partitions but also counts them with a closed formula. Also we enumerate
-core partitions with corners and self-conjugate
-core partitions.Comment: 11 page