Computational proofs of congruences for 2-colored Frobenius partitions

Computational proofs of congruences for 2-colored Frobenius partitions

In 1994, the following infinite family of congruences was conjectured for the partition function cΦ2(n) which counts the number of 2-colored Frobenius partitions of n: for all n≥0 and α≥1, cΦ2(5αn+λα)≡0(mod5α), where λα is the least positive reciprocal of 12 modulo 5α. In this paper, the first four...

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Main Authors: Dennis Eichhorn, James A. Sellers
Format: Article
Language:English
Published: Hindawi Limited 2002-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171202007342
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spelling doaj-843f5c5da6cd454683b4575d6d2c5a5b2020-11-24T22:30:40ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0129633334010.1155/S0161171202007342Computational proofs of congruences for 2-colored Frobenius partitionsDennis Eichhorn0James A. Sellers1Department of Mathematics, University of Arizona, Tucson, AZ 85721, USADepartment of Mathematics, Penn State University, University Park, PA 16802, USAIn 1994, the following infinite family of congruences was conjectured for the partition function cΦ2(n) which counts the number of 2-colored Frobenius partitions of n: for all n≥0 and α≥1, cΦ2(5αn+λα)≡0(mod5α), where λα is the least positive reciprocal of 12 modulo 5α. In this paper, the first four cases of this family are proved.http://dx.doi.org/10.1155/S0161171202007342
collection DOAJ
language English
format Article
sources DOAJ
author Dennis Eichhorn
James A. Sellers
spellingShingle Dennis Eichhorn
James A. Sellers
Computational proofs of congruences for 2-colored Frobenius partitions
International Journal of Mathematics and Mathematical Sciences
author_facet Dennis Eichhorn
James A. Sellers
author_sort Dennis Eichhorn
title Computational proofs of congruences for 2-colored Frobenius partitions
title_short Computational proofs of congruences for 2-colored Frobenius partitions
title_full Computational proofs of congruences for 2-colored Frobenius partitions
title_fullStr Computational proofs of congruences for 2-colored Frobenius partitions
title_full_unstemmed Computational proofs of congruences for 2-colored Frobenius partitions
title_sort computational proofs of congruences for 2-colored frobenius partitions
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2002-01-01
description In 1994, the following infinite family of congruences was conjectured for the partition function cΦ2(n) which counts the number of 2-colored Frobenius partitions of n: for all n≥0 and α≥1, cΦ2(5αn+λα)≡0(mod5α), where λα is the least positive reciprocal of 12 modulo 5α. In this paper, the first four cases of this family are proved.
url http://dx.doi.org/10.1155/S0161171202007342
work_keys_str_mv AT denniseichhorn computationalproofsofcongruencesfor2coloredfrobeniuspartitions
AT jamesasellers computationalproofsofcongruencesfor2coloredfrobeniuspartitions
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