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Full-Text Articles in Mathematics
Communal Partitions Of Integers, Darren B. Glass
Communal Partitions Of Integers, Darren B. Glass
Math Faculty Publications
There is a well-known formula due to Andrews that counts the number of incongruent triangles with integer sides and a fixed perimeter. In this note, we consider the analagous question counting the number of k-tuples of nonnegative integers none of which is more than 1/(k−1) of the sum of all the integers. We give an explicit function for the generating function which counts these k-tuples in the case where they are ordered, unordered, or partially ordered. Finally, we discuss the application to algebraic geometry which motivated this question.
Generalized Borcea-Voisin Construction, Jimmy Dillies
Generalized Borcea-Voisin Construction, Jimmy Dillies
Department of Mathematical Sciences Faculty Publications
C. Voisin and C. Borcea have constructed mirror pairs of families of Calabi-Yau threefolds by taking the quotient of the product of an elliptic curve with a K3 surface endowed with a non-symplectic involution. In this paper, we generalize the construction of Borcea and Voisin to any prime order and build three and four dimensional Calabi-Yau orbifolds. We classify the topological types that are obtained and show that, in dimension 4, orbifolds built with an involution admit a crepant resolution and come in topological mirror pairs. We show that for odd primes, there are generically no minimal resolutions and the …
On Some Order 6 Non-Symplectic Automorphisms Of Elliptic K3 Surfaces, Jimmy J. Dillies
On Some Order 6 Non-Symplectic Automorphisms Of Elliptic K3 Surfaces, Jimmy J. Dillies
Department of Mathematical Sciences Faculty Publications
We classify primitive non-symplectic automorphisms of order 6 on K3 surfaces. We show how their study can be reduced to the study of non-symplectic automorphisms of order 3 and to a local analysis of the fixed loci. In particular, we determine the possible fixed loci and show that when the Picard lattice is fixed, K3 surfaces come in mirror pairs.