Give combinatorial or bijective proofs of the following. Part of your job is to deter- mine...

 

Transcribed Image Text:

Give combinatorial or bijective proofs of the following. Part of your job is to deter- mine all values of n, k, and/or m for which the identities are valid. n (2) 3" = = k=0 n k n 2n-k k n -(0)-(0)-)) k 0 = 1 2 k n = *(Q) + (A)+()+(0)-(6) (d) m n m m (c) = ( ). - k - m = m+ (m 1). (f) - - ( ~ ) + ( ~ ) + ( ) ( ) ( ) - + = - (c). n (xx) - ( + - (e) k - n)) 2 ) 3 Give combinatorial or bijective proofs of the following. Part of your job is to deter- mine all values of n, k, and/or m for which the identities are valid. n (2) 3" = = k=0 n k n 2n-k k n -(0)-(0)-)) k 0 = 1 2 k n = *(Q) + (A)+()+(0)-(6) (d) m n m m (c) = ( ). - k - m = m+ (m 1). (f) - - ( ~ ) + ( ~ ) + ( ) ( ) ( ) - + = - (c). n (xx) - ( + - (e) k - n)) 2 ) 3