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GarcíaSegador, P. and Miranda Menéndez, Pedro (2018) BottomUp: a New Algorithm to Generate Random Linear Extensions of a Poset. Order . pp. 126. ISSN 01678094

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Official URL: https://doi.org/10.1007/s1108301894761
URL  URL Type 

https://link.springer.com/journal/11083  UNSPECIFIED 
Abstract
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.
Item Type:  Article 

Uncontrolled Keywords:  Poset, Linear extension, Random generation, Probability 
Subjects:  Sciences > Mathematics > Functional analysis and Operator theory Sciences > Mathematics > Probabilities 
ID Code:  54907 
Deposited On:  04 Apr 2019 17:23 
Last Modified:  09 Oct 2019 23:01 
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