Geodesic
Decomposition of the product of a monomial and a Demazure atom
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020).

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We prove that the product of a monomial and a Demazure atom is a positive sum of Demazure atoms combinatorially. This result proves one particular case in a conjecture which provides an approach to a combinatorial proof of Schubert positivity property. 
@article{DMTCS_2020_special_379_a5,
     author = {Ying Pun, Anna},
     title = {Decomposition of the product of a monomial and a {Demazure} atom},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)},
     year = {2020},
     doi = {10.46298/dmtcs.6323},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6323/}
}
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Ying Pun, Anna. Decomposition of the product of a monomial and a Demazure atom. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020). doi : 10.46298/dmtcs.6323. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6323/

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