2005/09/13 by Maurice Pouzet, Pouzet, Maurice, Nejib Zaguia +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #I.1.2 #I.4.10 #I.5 #Mathematical Dynamics and Fractals #cs.DM #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.cs/0509034
7 pages, 4 pictures
arxiv created 2005/09/13 · openalex publication_date 2005/09/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let S_N(P) be the poset obtained by adding a dummy vertex on each diagonal edge of the N's of a finite poset P. We show that S_N(S_N(P)) is N-free. It follows that this poset is the smallest N-free barycentric subdivision of the diagram of P, poset whose existence was proved by P.A. Grillet. This is also the poset obtained by the algorithm starting with P_0:=P and consisting at step m of adding a dummy vertex on a diagonal edge of some N in P_m, proving that the result of this algorithm does not depend upon the particular choice of the diagonal edge choosen at each step. These results are linked to drawing of posets.