Geodesic
Bijections and congruences for generalizations of partition identities of Euler and Guy
The electronic journal of combinatorics, Tome 11 (2004) no. 1
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In 1958, Richard Guy proved that the number of partitions of $n$ into odd parts greater than one equals the number of partitions of $n$ into distinct parts with no powers of 2 allowed, which is closely related to Euler's famous theorem that the number of partitions of $n$ into odd parts equals the number of partitions of $n$ into distinct parts. We consider extensions of Guy's result, which naturally lead to a new algorithm for producing bijections between various equivalent partition ideals of order 1, as well as to two new infinite families of parity results which follow from Euler's Pentagonal Number Theorem and a well-known series-product identity of Jacobi.
DOI : 10.37236/1796
Classification : 05A17, 11P83
Mots-clés : Euler's theorem, number of partitions, identity of Jacobi 
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     author = {James A. Sellers and Andrew V. Sills and Gary L. Mullen},
     title = {Bijections and congruences for generalizations of partition identities of {Euler} and {Guy}},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {1},
     doi = {10.37236/1796},
     zbl = {1058.05006},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1796/}
}
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James A. Sellers; Andrew V. Sills; Gary L. Mullen. Bijections and congruences for generalizations of partition identities of Euler and Guy. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1796

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