https://hal.inria.fr/hal-01229661Striker, JessicaJessicaStrikerUMN-MATH - School of Mathematics - UMN - University of Minnesota [Twin Cities] - University of Minnesota SystemA bijection between permutations and a subclass of TSSCPPsHAL CCSD2013alternating sign matrixplane partitionpermutationbijection[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]Monteil, AlainAlain Goupil and Gilles Schaeffer2015-11-17 10:19:292021-05-06 09:44:042015-11-17 10:25:14enConference papershttps://hal.inria.fr/hal-01229661/document10.46298/dmtcs.2344application/pdf1We 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.