The Ramanujan Journal

, Volume 23, Issue 1–3, pp 335–339 | Cite as

Column-to-row operations on partitions: Garden of Eden partitions

Article
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Abstract

Conjugation and the Bulgarian solitaire move are the extreme cases of general column-to-row operations on integer partitions. Each operation generates a state diagram on the partitions of n. Garden of Eden states are those with no preimage under the operation in question. In this note, we determine the number of Garden of Eden partitions for all n and column-to-row operations.

Keywords

Partitions Bulgarian solitaire 

Mathematics Subject Classification (2000)

05A17 37E15 
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References

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    Hopkins, B.: Column-to-row operations on partitions: the envelopes. In: Combinatorial Number Theory, Proceedings in Mathematics, pp. 65–76. de Gruyter, Berlin (2009). Also available in Integers 9 Supplement, Article 6 (2009) Google Scholar
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    Hopkins, B., Sellers, J.: Exact enumeration of Garden of Eden partitions. Integers 7(2), A19 (2007) Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsSaint Peter’s CollegeJersey CityUSA
  2. 2.Department of MathematicsUniversity of Tennessee at MartinMartinUSA

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