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In algebraic statistics it is common to use toric ideals to
study graph
models. If there are $r$ possible outcome of every random
variable of the
model, and the graph has $n$ vertices, then the toric ideal
will live in a
huge ring with $r^n$ variables. For computational and
theoretical purposes
it is desirable to cut down the size of the ring while
preserving some
properties of the toric ideals. To achieve this we have
introduced the
ideals of graph homomorphisms.
In this talk I will give an introduction to the ideals of graph homomorphism and explain their use in algebraic statistics. This is joint work with Patrik Norén at KTH. |