Statistics on bargraphs of inversion sequences of permutations
Abstract
We consider the joint distribution of the area and perimeter statistics on the set In of inversion sequences of length n represented as bargraphs. Functional equations for both the ordinary and exponential generating functions are derived from recurrences satisfied by this distribution. Explicit formulas are found in some special cases as are expressions for the totals of the respective statistics on In. A similar treatment is provided for the joint distribution on In for the statistics recording the number of levels, descents and ascents. Some connections are made between specific cases of this latter distribution and the Stirling numbers of the first kind and Eulerian numbers.
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