Within the palace complex in Alexandria, the city founded by Alexander in Egypt, a community of scholars was established in what was known as the Museum (or Mouseion); linked to this was a library, the Great Library of Alexandria. These two institutions are often celebrated for their role in the history of scholarship, but they were also the products of the Hellenistic age and of the competition which arose between the successors of Alexander. In many ways these two institutions encapsulate the ideology and policy of the early Ptolemies. It is the purpose of this paper to explore this aspect and set them in a wider context.

A graph is closed when its vertices have a labeling by [n] with a certain property first discovered in the study of binomial edge ideals. In this article, we prove that a connected graph has a closed labeling if and only if it is chordal, claw-free, and has a property we call narrow, which holds when every vertex is distance at most one from all longest shortest paths of the graph.

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The origins of the well-known hatred for the nomen regis at Rome are in this way explained by Cicero in the De Republica, written in the late 50s b.c. Tarquinius Superbus, Rome's last king, so traumatised the Roman people that the term rex still had a potent effect almost five hundred years after his downfall. Many modern scholars would accept that the Roman hatred of kings was deep-rooted and intense, and it is often called upon to explain Roman behaviour. This approach finds clear expression in the latest edition of the Cambridge Ancient History, where one scholar in his discussion of the overthrow of Tarquinius writes: ‘Forever after the Romans hated the very idea of a king’. Yet an examination of Latin writings from the Republican period, rather than confirming this, reveals much that is at odds with this interpretation of the Roman attitude towards kings and the concept of kingship. Surprisingly, even their own kings are generally treated favourably. While there is no doubt that there was hostility to kings in the first century b.c., it is necessary to reconsider its origins and nature. I wish to argue that it was neither as long-standing nor as intense as is traditionally assumed. Its origins should be sought not in the distant obscurity of the last years of the regal period, but in Rome's encounters with the hellenistic kings of the East in the second century b.c.