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.

Partitions of a Finite Partially Ordered Set / P. Codara - In: From combinatorics to philosophy : the legacy of G.-C. Rota / [a cura di] E. Damiani, O. D'Antona, V. Marra, F. Palombi. - New York : Springer, 2009. - ISBN 9780387887524. - pp. 45-59

Partitions of a Finite Partially Ordered Set

P. Codara
Primo
2009

Abstract

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.
Partition ; Partially Ordered Set ; Category
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/72736
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