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...
View ArticleAn 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 \(M \times N\)...
View ArticleA 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’...
View ArticleUnification, 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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