Jessica Striker - A bijection between permutations and a subclass of TSSCPPs

dmtcs:2344 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.2344
A bijection between permutations and a subclass of TSSCPPs

Authors: Jessica Striker 1

  • 1 School of Mathematics

We define a subclass of totally symmetric self-complementary plane partitions (TSSCPPs) which we show is in direct bijection with permutation matrices. This bijection maps the inversion number of the permutation, the position of the 1 in the last column, and the position of the 1 in the last row to natural statistics on these TSSCPPs. We also discuss the possible extension of this approach to finding a bijection between alternating sign matrices and all TSSCPPs. Finally, we remark on a new poset structure on TSSCPPs arising from this perspective which is a distributive lattice when restricted to permutation TSSCPPs.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: alternating sign matrix,plane partition,permutation,bijection,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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Source : ScholeXplorer IsRelatedTo DOI 10.1016/0097-3165(94)90048-5
  • 10.1016/0097-3165(94)90048-5
Plane partitions V: the TSSCPP conjecture

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