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Weighted Counting of Inversions on Alternating Sign Matrices

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Abstract

We generalize the author’s formula (2011) on weighted counting of inversions on permutations to one on alternating sign matrices. The proof is based on the sequential construction of alternating sign matrices from the unit matrix which essentially follows from the earlier work of Lascoux-Schützenberger (1996).

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Acknowledgments

The author would like to thank the editor Nathan Reading and the anonymous referee for many helpful comments and suggestions to improve the manuscript.

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Correspondence to Masato Kobayashi.

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Appendix

Appendix

Table 1 16 types of covering relations \(A\lhd B\) in \(\mathcal {A}_{n}\)
Fig. 3
figure 3

\((\mathcal {A}_{4}, \lhd )\) with 10 bigrassmannian permutations

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Kobayashi, M. Weighted Counting of Inversions on Alternating Sign Matrices. Order 37, 461–477 (2020). https://doi.org/10.1007/s11083-019-09515-1

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