• Corpus ID: 218889259

Alternating sign matrices and totally symmetric plane partitions

@article{Aigner2020AlternatingSM,
  title={Alternating sign matrices and totally symmetric plane partitions},
  author={Florian Aigner and Ilse Fischer and Matjavz Konvalinka and Philippe Nadeau and Vasu Tewari},
  journal={arXiv: Combinatorics},
  year={2020}
}
We study the Schur polynomial expansion of a family of symmetric polynomials related to the refined enumeration of alternating sign matrices with respect to their inversion number, complementary inversion number and the position of the unique $1$ in the top row. We prove that the expansion can be expressed as a sum over totally symmetric plane partitions and we are also able to determine the coefficients. This establishes a new connection between alternating sign matrices and a class of plane… 
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