RT Journal Article
T1 Bottom-Up: a New Algorithm to Generate Random Linear Extensions of a Poset
A1 García-Segador, P.
A1 Miranda Menéndez, Pedro
AB In this paper we present a new method for deriving a random linear extension of a poset. This new strategy combines Probability with Combinatorics and obtains a procedure where each minimal element of a sequence of subposets is selected via a probability distribution. The method consists in obtaining a weight vector on the elements of P, so that an element is selected with a probability proportional to its weight. From some properties on the graph of adjacent linear extensions, it is shown that the probability distribution can be obtained by solving a linear system. The number of equations involved in this system relies on the number of what we have called positioned antichains, that allows a reduced number of equations. Finally, we give some examples of the applicability of the algorithm. This procedure cannot be applied to every poset, but it is exact when it can be used. Moreover, the method is quick and easy to implement. Besides, it allows a simple way to derive the number of linear extensions of a given poset.
PB Springer Netherlands
SN 0167-8094
YR 2018
FD 2018-10-09
LK https://hdl.handle.net/20.500.14352/13212
UL https://hdl.handle.net/20.500.14352/13212
LA eng
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NO Ministerio de Economía y Competitividad (MINECO)
DS Docta Complutense
RD 29 abr 2024