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- Lior Pachter, David E Speyer
- Appl. Math. Lett.
- 2004

The tree-metric theorem provides a necessary and sufficient condition for a dissimilarity matrix to be a tree metric, and has served as the foundation for numerous distance-based reconstruction methods in phy-logenetics. Our main result is an extension of the tree-metric theorem to more general dissimilarity maps. In particular, we show that a tree with n… (More)

- T. Kyle Petersen, David E Speyer
- J. Comb. Theory, Ser. A
- 2005

In earlier work, Jockusch, Propp, and Shor proved a theorem describing the limiting shape of the boundary between the uniformly tiled corners of a random tiling of an Aztec diamond and the more unpredictable 'temperate zone' in the interior of the region. The so-called arctic circle theorem made precise a phenomenon observed in random tilings of large Aztec… (More)

- David E Speyer, Zsuzsanna Szaniszló
- Discrete Mathematics
- 2000

- David E Speyer
- 2005

Barot, Geiss and Zelevinsky define a notion of a " cyclically orientable graph " and use it to devise a test for whether a cluster algebra is of finite type. Barot, Geiss and Zelivinsky's work leaves open the question of giving an efficient characterization of cyclically orientable graphs. In this paper, we give a simple recursive description of cyclically… (More)

A central appeal of algebraic geometry is that its functions are polynomi-als which can be written down as finite expressions. This makes the theory naturally combinatorial, in that polynomials are made up of a finite number of terms which interact through discrete rules. In practice, however, the operations performed on these polynomials are usually too… (More)

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