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On generalizations of partition theorems of Schur and Andrews to overpartitions

AbstractIn this paper, we give three new proofs of Schur’s theorem for overpartitions using recurrences and generating functions. We also prove two new theorems on overpartitions with difference...

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An overpartition analogue of the q -binomial coefficients

AbstractWe define an overpartition analogue of Gaussian polynomials (also known as q-binomial coefficients) as a generating function for the number of overpartitions fitting inside the \(M \times N\)...

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A generalisation of a partition theorem of Andrews

AbstractAndrews (Am J Math 91:18–24, 1969) proved a theorem on partitions with difference conditions which generalises Schur’s celebrated partition identity. In this paper, we generalise Andrews’...

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Unification, Refinements and Companions of Generalisations of Schur’s Theorem

AbstractWe prove a general theorem on coloured overpartitions with difference conditions that unifies generalisations of Schur’s theorem due to Alladi–Gordon, Andrews, Corteel–Lovejoy, Lovejoy and the...

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