Orders for Simplifying Partial Partitions

Orders on Partial Partitions and Maximal Partitioning of Sets

(*) This work received funding from the Agence Nationale de la Recherche through contract ANR-2010-BLAN-0205-01 " KIDICO " .

Deriving Bisimulations by Simplifying Partitions

In this paper we analyze the problem of transforming partitions in order to satisfy completeness in the standard abstract interpretation framework. In order to obtain this, we exploit the relation existing between completeness and the Paige-Tarjan notion of stability, already detected in the particular context of refining partitions for completeness. Here we extend this relation in order to cop...

Partial Orders on Partial Isometries

This paper studies three natural pre-orders of increasing generality on the set of all completely non-unitary partial isometries with equal defect indices. We show that the problem of determining when one partial isometry is less than another with respect to these pre-orders is equivalent to the existence of a bounded (or isometric) multiplier between two natural reproducing kernel Hilbert spac...

All orders asymptotic expansion of large partitions

The generating function which counts partitions with the Plancherel measure (and its q-deformed version), can be rewritten as a matrix integral, which allows to compute its asymptotic expansion to all orders. There are applications in statistical physics of growing/melting crystals, T.A.S.E.P., and also in algebraic geometry. In particular we compute the Gromov-Witten invariants of the Xp = O(p...

Extending Partial Orders to Dense Linear Orders