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math.CO2018
Revisiting pattern avoidance and quasisymmetric functions
Jonathan Bloom, Bruce Sagan
Let S_n be the nth symmetric group. Given a set of permutations Pi we denote by S_n(Pi) the set of permutations in S_n which avoid Pi in the sense of pattern avoidance. Consider th…
math.CO2018
Rook and Wilf equivalence of integer partitions
Jonathan Bloom, Dan Saracino
The subjects of rook equivalence and Wilf equivalence have both attracted considerable attention over the last half-century. In this paper we introduce a new notion of Wilf equival…
math.CO2018
On criteria for rook equivalence of Ferrers boards
Jonathan Bloom, Dan Saracino
In [2] we introduced a new notion of Wilf equivalence of integer partitions and proved that rook equivalence implies Wilf equivalence. In the present paper we prove the converse an…