Combinatorics
Lah numbers and Lindström's lemma
Comptes Rendus. Mathématique, Volume 356 (2018) no. 1, pp. 5-7.

We provide a combinatorial interpretation of Lah numbers by means of planar networks. Henceforth, as a consequence of Lindström's lemma, we conclude that the related Lah matrix possesses a remarkable property of total non-negativity.

Nous donnons une interprétation combinatoire des nombres de Lah en termes de réseaux plans. Puis, comme conséquence du lemme de Lidström, nous en déduisons que la matrice de Lah associée possède la propriété remarquable d'être totalement non négative.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2017.11.010
Martinjak, Ivica 1; Škrekovski, Riste 2, 3, 4

1 Faculty of Science, University of Zagreb, Zagreb, Croatia
2 Faculty of Information Studies, Novo Mesto, Slovenia
3 FMF, University of Ljubljana, Ljubljana, Slovenia
4 FAMNIT, University of Primorska, Slovenia
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Martinjak, Ivica; Škrekovski, Riste. Lah numbers and Lindström's lemma. Comptes Rendus. Mathématique, Volume 356 (2018) no. 1, pp. 5-7. doi : 10.1016/j.crma.2017.11.010. http://www.numdam.org/articles/10.1016/j.crma.2017.11.010/

[1] Fomin, S.; Zelevinsky, A. Total positivity: test and parametrizations, Math. Intell., Volume 22 (2000), pp. 23-33

[2] Kung, J.; Rota, G.; Yan, C. Combinatorics: The Rota Way, Cambridge University Press, Cambridge, UK, 2009

[3] Ramirez, C.; Shattuck, M. A (p,q)-analogue of the r-Whitney–Lah numbers, J. Integer Seq., Volume 19 (2016) (Article 16.5.6)

[4] Wagner, C. Generalized Stirling and Lah numbers, Discrete Math., Volume 160 (1996), pp. 199-218

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