Araucaria Cones

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Shuffle of Words and Araucaria Trees

The shuffle of words ,. . . , is the set of words obtained by interleaving the letters of these words such that the order of appearance of all letters of each word is respected. The study of the shuffle product of words leads to the construction of an automaton whose structure is deeply connected to a family of trees which we call araucarias. We prove many structural properties of this family o...

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Araucaria Trees: Construction and Grafting Theorems

Araucarias have been introduced by Schott and Spehner as trees which appear in the minimal automaton of the shuffle of words. We give here a new definition of araucarias which is more constructive and we prove that our definition of araucarias is equivalent to the original one. From the new definition we derive an optimal algorithm for the construction of araucarias and a new method for calcula...

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Evolutionary Diversification of New Caledonian Araucaria

New Caledonia is a global biodiversity hotspot. Hypotheses for its biotic richness suggest either that the island is a 'museum' for an old Gondwana biota or alternatively it has developed following relatively recent long distance dispersal and in situ radiation. The conifer genus Araucaria (Araucariaceae) comprises 19 species globally with 13 endemic to this island. With a typically Gondwanan d...

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Indecomposable Cones

We study some relations between a reproducing cone K in a linear space V over a fully ordered field F and the cone I(K) in Hom( V, V) consisting of all operators A such that AK G K. In particular, indecomposable cones are considered.

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ژورنال

عنوان ژورنال: Nature

سال: 1890

ISSN: 0028-0836,1476-4687

DOI: 10.1038/043057b0