Partitions of a Finite Partially Ordered Set

نویسنده

  • Pietro Codara
چکیده

In this paper, we investigate the notion of partition of a finite partially ordered set (poset, for short). We will define three different notions of partition of a poset, namely, monotone, regular, and open partition. For each of these notions we will find three equivalent definitions, that will be shown to be equivalent. We start by defining partitions of a poset in terms of fibres of some surjection having the poset as domain. We then obtain combinatorial characterisations of such notions in terms of blocks, without reference to surjection. Finally, we give a further, equivalent definition of each kind of partition by means of analogues of equivalence relations.

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عنوان ژورنال:
  • CoRR

دوره abs/1307.1615  شماره 

صفحات  -

تاریخ انتشار 2013