Remark about

The author is asking about Homomorphism of FLin. In section 4.4.4 he talks about morphism of orders. If s1 <= s2 then f(s1) <= f(s2). Also, order is reflexive (s <= s). So when we have a morphism from FLin[2] to FLin[3] we need to pick 3 elements in FLin[3] so that they are related like they were in FLin[2]. The 3 elements we need to map are 0, 1, 2. If we map 0 in FLin[2] to 3 in FLin[3] then

f(0) = 3

In FLin[2] 0 <= 1. So f(0) <= f(1). If f(0) is 3 then f(1) and f(2) has to be 3 for f(0) <= f(1) and f(0) <= f(2) and f(1) <= f(2). Basically we need to find 3 non decreasing elements in FLin[3]. Rest is combinatorics.

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