Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 northst 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 re mainly algebraic in nature.  give two combinatorial proofs of this theorem.
['Miklós Bóna', 'Bruce E. Sagan']
I am writing a research paper on a idea Two injective proofs of a conjecture of Simion
[{"from": "human", "value": "I am writing a research paper on a idea Two injective proofs of a conjecture of Simion"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 northst 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 re mainly algebraic in nature.  give two combinatorial proofs of this theorem."}]