Some enumeration relating to intervals in posets. (English) Zbl 1540.06002
Cunningham, Gabriel (ed.) et al., Polytopes and discrete geometry. AMS special session, Northeastern University, Boston, MA, USA, April 21–22, 2018. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 764, 149-155 (2021).
Summary: Given a finite ranked poset \(P\) another, \(\mathcal{J}(P)\), is obtained by considering its poset of intervals. Iteration of this construction yields a sequence of ranked posets. The functions giving the number of elements of given rank in \(\mathcal{J}^k(P)\) is studied by utilizing the notion of parity representation of posets. It is shown that these functions are given by polynomials in \(2^k\).
For the entire collection see [Zbl 1467.52001].
For the entire collection see [Zbl 1467.52001].
MSC:
| 06A07 | Combinatorics of partially ordered sets |
| 05A15 | Exact enumeration problems, generating functions |
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