Suppose $P$ is a rank $r$ poset. For each strictly increasing sequence $(i_1, \ldots, i_k)$ with $0 \leq i_j \leq i_k$, the coefficient of $q_i_1 \cdots q_i_k$ is the number of flagChains in the ranks $i_1, \cdots, i_k$.
The flag-f polynomial of the $n$ chain is $(q_0 + 1)\cdots(q_{n-1}+1)$.
i1 : n = 4; |
i2 : factor flagfPolynomial chain n
o2 = (q + 1)(q + 1)(q + 1)(q + 1)
3 2 1 0
o2 : Expression of class Product
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The object flagfPolynomial is a method function with options.