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Possible database queries for Dyck paths: search your data / browse all statistics / browse all maps

1. Definition & Example

Equivalently, a Dyck path of semilength $n$ can be seen as

The five Dyck paths of semilength 3

http://www.findstat.org/Graphics/api/Cc0005_0_[1,0,1,0,1,0].png

http://www.findstat.org/Graphics/api/Cc0005_0_[1,0,1,1,0,0].png

http://www.findstat.org/Graphics/api/Cc0005_0_[1,1,0,0,1,0].png

http://www.findstat.org/Graphics/api/Cc0005_0_[1,1,0,1,0,0].png

http://www.findstat.org/Graphics/api/Cc0005_0_[1,1,1,0,0,0].png

 [1,0,1,0,1,0] 

 [1,0,1,1,0,0] 

 [1,1,0,0,1,0] 

 [1,1,0,1,0,0] 

 [1,1,1,0,0,0] 

2. Properties

3. Remarks

4. References

[Ath04]   C.A. Athanasiadis, Generalized Catalan numbers, Weyl groups and arrangements of hyperplanes, Bull. London Math. Soc., 36 (2004), pp. 294-392.

[Kra89]   C. Krattenthaler, Counting <strong class="highlight">lattice</strong> <strong class="highlight">paths</strong> with a linear boundary II, Sitz.ber. d. ÖAW Math.-naturwiss. Klasse 198 (1989), 171-199.

5. Sage examples

6. Technical information for database usage