Abstract:The study of flattened partitions is an active area of current research. In this paper, our study unexpectedly leads us to the OEIS numbers A124324. We provide a new combinatorial interpretation of these numbers. A combinatorial bijection between flattened partitions over [n + 1] and the partitions of [n] is also given in a separate section. We introduce the numbers f n,k which count the number of flattened partitions over [n] having k runs. We give recurrence relations defining them, as well as their exponent… Show more
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