The set of autotopisms of partial Latin squares

Symmetries of a partial Latin square are determined by its autotopism group. Analogously to the case of Latin squares, given an isotopism $\Theta$, the cardinality of the set $\mathcal{PLS}_{\Theta}$ of partial Latin squares which are invariant under $\Theta$ only depends on the conjugacy class of the latter, or, equivalently, on its cycle structure. In the current paper, the cycle structures of the set of autotopisms of partial Latin squares are characterized and several related properties studied. It is also seen that the cycle structure of $\Theta$ determines the possible sizes of the elements of $\mathcal{PLS}_{\Theta}$ and the number of those partial Latin squares of this set with a given size. Finally, it is generalized the traditional notion of partial Latin square completable to a Latin square.Comment: 20 pages, 4 table

A SAURON look at galaxy bulges

Kinematic and population studies show that bulges are generally rotationally flattened systems similar to low-luminosity ellipticals. However, observations with state-of-the-art integral field spectrographs, such as SAURON, indicate that the situation is much more complex, and allow us to investigate phenomena such as triaxiality, kinematic decoupling and population substructure, and to study their connection to current formation and evolution scenarios for bulges of early-type galaxies. We present the examples of two S0 bulges from galaxies in our sample of nearby galaxies: one that shows all the properties expected from classical bulges (NGC5866), and another case that presents kinematic features appropriate for barred disk galaxies (NGC7332).Comment: 4 pages, 3 figures, accepted for publishing in AN (refereed conf. proc. of the Euro3D Science workshop, IoA Cambridge, May 2003

Towards a new classification of early-type galaxies: an integral-field view

In this proceeding we make use of the two-dimensional stellar kinematics of a representative sample of E and S0 galaxies obtained with the SAURON integral-field spectrograph to reveal that early-type galaxies appear in two broad flavours, depending on whether they exhibit clear large-scale rotation or not. We measure the level of rotation via a new parameter LambdaR and use it as a basis for a new kinematic classification that separates early-type galaxies into slow and fast rotators. With the aid of broad-band imaging we will reinforce this finding by comparing our kinematic results to the photometric properties of these two classes.Comment: 4 pages, 2 figures, to appear in "Pathways Through an Eclectic Universe", J. H. Knappen, T. J. Mahoney, and A. Vazedekis (Eds.), ASP Conf. Ser., 200