Two injective proofs of a conjecture of Simion

Authors:
Miklós Bóna;Bruce E. Sagan
Affiliations:
Department of Mathematics, University of Florida, Little Hall, Gainesville, FL;Department of Mathematics, Michigan State University, East Lansing, MI
Venue:
Journal of Combinatorial Theory Series A
Year:
2003

Citing 4
Cited 0

Enumerative combinatorics

Enumerative combinatorics
Combinatorial statistics on non-crossing partitions

Journal of Combinatorial Theory Series A
Log concavity of a sequence in a conjecture of Simion

Journal of Combinatorial Theory Series A
A simple proof of a conjecture of Simion

Journal of Combinatorial Theory Series A

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Abstract

Simion (J. Combin. Theory Ser. A 94 (1994) 270) conjectured the unimodality of a sequence counting lattice paths in a grid with a Ferrers diagram removed from the northwest corner. Recently, Hildebrand (J. Combin. Theory Ser. A 97 (2002) 108) and then Wang (A simple proof of a conjecture of Simion, J. Combin. Theory Ser. A 100 (2002) 399) proved the stronger result that this sequence is actually log concave. Both proofs were mainly algebraic in nature. We give two combinatorial proofs of this theorem.