论文信息 - Two injective proofs of a conjecture of Simion

Two injective proofs of a conjecture of Simion

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.

Bruce E. Sagan | Miklós Bóna

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