no. 1
Combinatorics
Lah numbers and Lindström's lemma
[Nombres de Lah et lemme de Lindström]

Présenté par : the Editorial Board

Martinjak, Ivica1 ; Škrekovski, Riste2, 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
Comptes Rendus. Mathématique, Tome 356 (2018) no. 1, pp. 5-7.

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.

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.

Reçu le :
Accepté le :
Publié le :
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, Tome 356 (2018) no. 1, pp. 5-7. doi : 10.1016/j.crma.2017.11.010. http://archive.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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