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The Bruhat Order of Generalized Alternating Sign Matrices and its Rank
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We continue the investigations in [7] extending the Bruhat order on n × n alternating sign matrices to a more general setting. We show that the resulting partially ordered set is a lattice and also investigate its rank.
Abstract
We continue the investigations in [7] extending the Bruhat order on n × n alternating sign matrices to a more general setting. We show that the resulting partially ordered set is a lattice and also investigate its rank.
참고문헌 (10)
- D.M. Bressoud, "Proofs and Confirmations; The Story of the Alternating Sign Matrix Conjecture" (1999), Math. Assoc. America
- A. Bj¨orner, "Graduate Texts in Math. #231" (2003), Springer
- R. A. Brualdi, "Patterns of alternating sign matrices", Linear Algebra Appl, 438, pp.3967~3990 (2013)[DOI]
- R.A. Brualdi, "Alternating sign matrices and their Bruhat order", Discrete Math, 340, pp.1996~2019 (2017)[DOI]
- R.A. Brualdi, "Alternating sign matrices, extensions, and related cones", Adv. in Appl. Math, 86, pp.19~49 (2017)[DOI]
- R.A. Brualdi, "Alternating sign matrices: Extensions, K¨onigproperties, and primary sum-sequences", Graph and Combinatorics, 36, pp.63~92 (2020)[DOI]
- R.A. Brualdi, "A generalization of alternating sign matrices", J. Combin. Des, 23, pp.204~215 (2015)[DOI]
- R.A. Brualdi, "A generalized alternating sign matrices and signed permuation matrices", J. Korean Math. Soc, 58(4), pp.921~948 (2021)[DOI]
- R.A. Brualdi, "Completions of alternating sign matrices", Graphs and Combinatorics, 31(3), pp.507~522 (2015)[DOI]
- A. Lascoux, "Treillis et bases des groupes de Coxeter", Electron. J. Combin, 3(2), pp.27~ (1996)[DOI]
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