Séminaire Lotharingien de Combinatoire, B34l (1995), 19 pp.

Kimmo Eriksson, Svante Linusson

The Size of Fulton's Essential Set

Abstract. The essential set of a permutation was defined by Fulton as the set of southeast corners of the diagram of the permutation. In this paper we determine explicit formulas for the average size of the essential set in the two cases of arbitrary permutations and 321-avoiding permutations. Vexillary permutations are discussed too.

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