with B(3) = 3! and D(3) = 4 In this section we show that in the case n = 2m + 2 the poset P satisfies P ? = ? * ( ? (B 2m+1 )) for some integer ? ? 1 and in the case n = 2m + 1 ,
Consequently the poset P has the following binomial and Sheffer factorial functions. (i) B(k) = k! for 1 ? k ? 2m, and B(2m + 1) = ?(2m + 1)!, ii) D(1) = 1, D(k) = 2(k ? 1)! for 2 ? k ? 2m + 1, and D(2m + 2) = 2? ,
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