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Triangle of Narayana numbers T(n,k) = C(n-1,k-1)*C(n,k-1)/k with 1 <= k <= n, read by rows. Also called the Catalan triangle.
(history; published version)
#651 by Andrew Howroyd at Sun Sep 01 10:35:40 EDT 2024
STATUS

reviewed

approved

#650 by Joerg Arndt at Sun Sep 01 10:27:50 EDT 2024
STATUS

proposed

reviewed

#649 by Michel Marcus at Sun Sep 01 09:41:01 EDT 2024
STATUS

editing

proposed

#648 by Michel Marcus at Sun Sep 01 09:40:51 EDT 2024
LINKS

J.-C. Novelli and J.-Y. Thibon, <a href="https://web.archiveeudml.org/web/20090525043541/http://journals.impan.gov.pl/fm/Infdoc/193-3-1.html283024">Hopf algebras and dendriform structures arising from parking functions</a>, Fundamenta Mathematicae 193 (2007), pp. 189-241; <a href="http://arxiv.org/abs/math/0511200">arXiv version</a>, 0511200 [math.CO], 2005.

STATUS

proposed

editing

#647 by Stefano Spezia at Sun Sep 01 09:30:09 EDT 2024
STATUS

editing

proposed

#646 by Stefano Spezia at Sun Sep 01 09:28:42 EDT 2024
LINKS

Axel Bacher, Antonio Bernini, Luca Ferrari, Benjamin Gunby, Renzo Pinzani, and Julian West, <a href="http://dx.doi.org/10.1016/j.disc.2013.12.011">The Dyck pattern poset</a> , Discrete Math. 321 (2014), 12--23. MR3154009.

#645 by Stefano Spezia at Sun Sep 01 09:28:01 EDT 2024
LINKS

C. Bean, M. Tannock , and H. Ulfarsson, <a href="http://arxiv.org/abs/1512.08155">Pattern avoiding permutations and independent sets in graphs</a>, arXiv:1512.08155 [math.CO], 2015.

A. Bernini, L. Ferrari, R. Pinzani , and J. West, <a href="http://arxiv.org/abs/1303.3785">The Dyck pattern poset</a>, arXiv:1303.3785 [math.CO], 2013.

Jonathan M. Borwein, Armin Straub , and Christophe Vignat, <a href="http://carmamaths.org/resources/jon/dwalks.pdf">Densities of short uniform random walks, Part II: Higher dimensions</a>, Preprint, 2015.

R. De Castro, A. L. Ramírez , and J. L. Ramírez, <a href="http://arxiv.org/abs/1310.2449">Applications in Enumerative Combinatorics of Infinite Weighted Automata and Graphs</a>, arXiv:1310.2449 [cs.DM], 2013.

T. Doslic, D. Svrtan , and D. Veljan, <a href="http://dx.doi.org/10.1016/j.disc.2004.04.001">Enumerative aspects of secondary structures</a>, Discr. Math., 285 (2004), 67-82.

F. Hivert, J.-C. Novelli , and J.-Y. Thibon, <a href="https://arxiv.org/abs/math/0605262">Commutative combinatorial Hopf algebras</a>, arXiv:math/0605262 [math.CO], 2006.

A. Sapounakis, I. Tasoulas , and P. Tsikouras, <a href="http://dx.doi.org/10.1016/j.disc.2007.03.005">Counting strings in Dyck paths</a>, Discrete Math., 307 (2007), 2909-2924.

#644 by Stefano Spezia at Sun Sep 01 09:23:03 EDT 2024
LINKS

R. A. Sulanke, <a href="https://web.archive.org/web/2018041620233620180416202341/http://math.boisestate.edu/~sulanke/PAPERS/narayana3ADLcutpasteII.pdf">Moments, Narayana numbers and the cut and paste for lattice paths</a>

R. A. Sulanke, <a href="https://web.archive.org/web/20180416202336/http://math.boisestate.edu/~sulanke/recentpapindexPAPERS/narayana3ADL.htmlpdf">Three-dimensional Narayana and Schröder numbers</a>

#643 by Stefano Spezia at Sun Sep 01 09:20:50 EDT 2024
LINKS

R. A. Sulanke, <a href="https://web.archive.org/web/20180416202336/http://math.boisestate.edu/~sulanke/recentpapindexPAPERS/narayana3ADL.htmlpdf">Moments, Narayana numbers and the cut and paste for lattice paths</a>

#642 by Stefano Spezia at Sun Sep 01 09:17:25 EDT 2024
LINKS

Lara Pudwell, <a href="http://permutationpatterns.com/slides/Pudwell.pdf">On the distribution of peaks (and other statistics)</a>, 16th International Conference on Permutation Patterns, Dartmouth College, 2018. [Broken link]