**Problem of the Week**

**Math Club**

**BUGCAT 2020**

**Zassenhaus Conference**

**Hilton Memorial Lecture**

seminars:comb:abstract.200304zas

A *polygon* is a Hamiltonian circuit of the complete graph on n vertices. If we assign real-number ``lengths` to the edges, each polygon has a length (that is, a real number), which induces a linear quasiordering of the set of all polygons. We call such a quasiordering `

really are lengths. That is, we pick n points in Euclidean space E*realizable*.
Now suppose the ``lengths^{d}, (P_{i}) = (P_{1}, P_{2}, …, P_{n}), and define the length of edge ij to be the distance d(P_{i}, P_{j}). There are some obvious questions. Which realizable quasiorderings are realizable by points in E^{d}? One could allow some of the points to coincide, or not; these give different answers. Given points (P_{i}) , inducing a certain realizable quasiordering, which other realizable quasiorderings are realizable by points (Q_{i}) arbitrarily near (P_{i})? I will discuss these questions.

This will be a very informal talk with at most bits of hints of proof.

seminars/comb/abstract.200304zas.txt · Last modified: 2020/01/29 14:03 (external edit)

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