Discrete Applied Mathematics the Permutahedron of Series-parallel Posets

N-free posets as generalizations of series-parallel posets

N-free posets have recently taken some importance and motivated many studies. This class of posets introduced by Grillet [8] and Heuchenne [11] are very related to another important class of posets, namely the series-parallel posets, introduced by Lawler [12] and studied by Valdes et al. [21]. This paper shows how N-free posets can be considered as generalizations of series-parallel posets, by ...

Series-parallel posets and the Tutte polynomial

We investigate the Tutte polynomial f(P; t, z) of a series-parallel partially ordered set P. We show that f(P) can be computed in polynomial-time when P is series-parallel and that series-parallel posets having isomorphic deletions and contractions are themselves isomorphic. A formula forf’(P*) in terms off(P) is obtained and shows these two polynomials factor over Z[t, z] the same way. We exam...

Retractions onto series-parallel posets

The poset retraction problem for a poset P is whether a given poset Q containing P as a subposet admits a retraction onto P, that is, whether there is a homomorphism from Q onto P which fixes every element of P. We study this problem for finite series-parallel posets P. We present equivalent combinatorial, algebraic, and topological charaterisations of posets for which the problem is tractable,...

An algorithm for solving the jump number problem

First, Cogis and Habib (RAIRO Inform. 7Mor. 13 (1979), 3-18) solved the jump number problem for series-parallel partially ordered sets (posets) by applying the greedy algorithm and then Rival (Proc. Amer. Math. Sot. 89 (1983). 387-394) extended their result to N-free posets. The author (Order 1 (1984), 7-19) provided an interpretation of the latter result in the terms of arc diagrams of posets ...

Facets of the Generalized Permutahedron of a Poset