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Partitions of totally positive elements in real quadratic fields
 Stern, David ; Kala, Vítězslav (advisor) ; Gil Muñoz, Daniel (referee)
We consider the additive semigroup O+ K(+) of totally positive integers in a real quadratic field K = Q( √ D). We define on O+ K(+) the partition function pK(α) and de- velop an algorithm for computing pK(α) for different square-free D and different α ∈ O+ K. We then investigate the behaviour of pK(α), characterizing the square-free numbers D for which pK(α) attains the numbers 1 through 5. Finally, we prove a sufficient condition for the number 6 to be attainable by pK(α). 1
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