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Quadratic Forms and Four Partition Functions Modulo 3
-
Jeremy Lovejoy
and
Robert Osburn
Published/Copyright:
February 24, 2011
Abstract
Recently, Andrews, Hirschhorn and Sellers have proven congruences modulo 3 for four types of partitions using elementary series manipulations. In this paper, we generalize their congruences using arithmetic properties of certain quadratic forms.
Received: 2010-09-16
Accepted: 2010-10-09
Published Online: 2011-02-24
Published in Print: 2011-February
© de Gruyter 2011
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Articles in the same Issue
- Symmetries in Steinhaus Triangles and in Generalized Pascal Triangles
- Unbounded Discrepancy in Frobenius Numbers
- Combinatorial Interpretations of Convolutions of the Catalan Numbers
- Quadratic Forms and Four Partition Functions Modulo 3
- On Bases with a T-Order
- Van der Waerden's Theorem and Avoidability in Words
- On a Class of Ternary Inclusion-Exclusion Polynomials
Keywords for this article
Partitions;
overpartitions;
congruences;
binary quadratic forms;
sums of squares
Articles in the same Issue
- Symmetries in Steinhaus Triangles and in Generalized Pascal Triangles
- Unbounded Discrepancy in Frobenius Numbers
- Combinatorial Interpretations of Convolutions of the Catalan Numbers
- Quadratic Forms and Four Partition Functions Modulo 3
- On Bases with a T-Order
- Van der Waerden's Theorem and Avoidability in Words
- On a Class of Ternary Inclusion-Exclusion Polynomials
