Exact Enumeration of Garden of Eden Partitions
- Published in 2006
- Added on
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We give two proofs for a formula that counts the number of partitions of \(n\) that have rank −2 or less (which we call Garden of Eden partitions). These partitions arise naturally in analyzing the game Bulgarian solitaire, summarized in Section 1. Section 2 presents a generating function argument for the formula based on Dyson’s original paper where the rank of a partition is defined. Section 3 gives a combinatorial proof of the result, based on a bijection on Bressoud and Zeilberger.
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@article{ExactEnumerationOfGardenOfEdenPartitions, title = {Exact Enumeration of Garden of Eden Partitions}, abstract = {We give two proofs for a formula that counts the number of partitions of \(n\) that have rank −2 or less (which we call Garden of Eden partitions). These partitions arise naturally in analyzing the game Bulgarian solitaire, summarized in Section 1. Section 2 presents a generating function argument for the formula based on Dyson’s original paper where the rank of a partition is defined. Section 3 gives a combinatorial proof of the result, based on a bijection on Bressoud and Zeilberger.}, url = {https://www.emis.de/journals/INTEGERS/papers/a19int2005/a19int2005.Abstract.html https://www.emis.de/journals/INTEGERS/papers/a19int2005/a19int2005.pdf http://www.personal.psu.edu/jxs23/HS{\_}integers{\_}final.pdf}, year = 2006, author = {Brian Hopkins and James A. Sellers}, comment = {}, urldate = {2018-05-13}, collections = {Attention-grabbing titles,Easily explained,Combinatorics} }