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Description: |
Littlewood-Richardson (LR) coefficients arise as integer multiplicities
in the decomposition of products of Schur functions. The hive model is introduced
as a means of evaluating these coefficients combinatorially. By using edge rather
than vertex labelling of LR-hives it is shown that LR-coefficients are non-zero if and
only if a set of essential Horn inequalities are satisfied. It is further shown that the
saturation of any one such inequality leads to a factorisation of the corresponding
LR-coefficients.
Stretched LR-coefficients are defined by scaling all parts of the partitions labelling
the three relevant Schur functions. It is known that stretched LR-coefficients are
polynomial in the stretching parameter. If time permits some properties and open
problems regarding the nature of these polynomials will be discussed.
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