# 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…

## One Citation

### Alternating sign matrices with reflective symmetry and plane partitions: $n+3$ pairs of equivalent statistics

- Mathematics
- 2022

. Vertically symmetric alternating sign matrices (VSASMs) of order 2 n + 1 are known to be equinumerous with lozenge tilings of a hexagon with side lengths 2 n + 2 , 2 n, 2 n + 2 , 2 n, 2 n + 2 , 2 n…

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