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no. 6
Smith normal form of matrices associated with differential posets
Shah, Syed Waqar Ali1
1 Lahore University of Management Sciences Department of Mathematics Lahore 54792 (Pakistan)
Algebraic Combinatorics, Volume 7 (2024) no. 6, pp. 1887-1899

We prove a conjecture of Miller and Reiner on the existence of Smith normal form for the DU-operators for a certain class of r-differential posets.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.393
Classification: 06A11, 15A21, 05E99
Keywords: differential poset, Smith normal form, canonical forms, invariant factor decomposition

Shah, Syed Waqar Ali 1

1 Lahore University of Management Sciences Department of Mathematics Lahore 54792 (Pakistan)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Shah, Syed Waqar Ali. Smith normal form of matrices associated with differential posets. Algebraic Combinatorics, Volume 7 (2024) no. 6, pp. 1887-1899. doi: 10.5802/alco.393

[1] Cai, T. W.; Stanley, R. P. The Smith normal form of a matrix associated with Young’s lattice, Proc. Amer. Math. Soc., Volume 143 (2015) no. 11, pp. 4695-4703 | DOI | MR | Zbl

[2] Dummit, D. S.; Foote, R. M. Abstract algebra, John Wiley & Sons, Inc., Hoboken, NJ, 2004, xii+932 pages | MR

[3] Miller, A. R.; Reiner, V. Differential posets and Smith normal forms, Order, Volume 26 (2009) no. 3, pp. 197-228 | DOI | MR | Zbl

[4] Pohst, M.; Zassenhaus, H. Algorithmic algebraic number theory, Encyclopedia of Mathematics and its Applications, 30, Cambridge University Press, Cambridge, 1997, xiv+499 pages | MR

[5] Stanley, R. P. Differential posets, J. Amer. Math. Soc., Volume 1 (1988) no. 4, pp. 919-961 | DOI | MR | Zbl

[6] Stanley, Richard P. Smith normal form in combinatorics, J. Combin. Theory Ser. A, Volume 144 (2016), pp. 476-495 | DOI | MR | Zbl

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