A348351 Number of permutations of [n] avoiding the patterns 2-41-3, 3-14-2, 2-14-3, and 3-41-2.

1, 1, 2, 6, 20, 72, 274, 1088, 4470, 18884, 81652, 360054, 1614618, 7346688, 33856008, 157777908, 742637416

Offset: 0

Author

Manfred Scheucher, Oct 20 2021

Keywords

• nonn
• more

Comments

Also the number of one-sided rectangulations.

References

• L. J. Leifheit, Combinatorial Properties of Rectangulations, Master's thesis, Technische Universität Berlin, 2021.

Links

• A. Asinowski, G. Barequet, M. Bousquet-Mélou, T. Mansour, and R. Y. Pinter, Orders induced by segments in floorplan partitions and (2-14-3,3-41-2)-avoiding permutations, Electronic Journal of Combinatorics 20(2), 2013.
• Andrei Asinowski, Jean Cardinal, Stefan Felsner, and Éric Fusy, Combinatorics of rectangulations: Old and new bijections, arXiv:2402.01483 [math.CO], 2023. See p. 30.
• D. Eppstein, E. Mumford, B. Speckmann, and K. Verbeek, Area-Universal Rectangular Layouts, arXiv:0901.3924 [cs.CG], 2009.
• A. Merino and T. Mütze, Combinatorial generation via permutation languages. III. Rectangulations, arXiv:2103.09333 [math.CO], 2021.
• Manfred Scheucher, L.J. Leifheit's python program for enumeration.
• The Combinatorial Object Server, Rectangulation Generator.

Crossrefs

Cf. A001181, A006318, A078482.

Extensions

Name corrected by Manfred Scheucher, May 24 2023

a(0)=1 prepended by Alois P. Heinz, Feb 05 2024