Name
Abstract | ||
|---|---|---|
The Tamari lattices have been intensely studied since their introduction by Dov Tamari around 1960. However oddly enough, a formula for the number of maximal chains is still unknown. This is due largely to the fact that maximal chains in the n th Tamari lattice T n range in length from n - 1 to n 2 . In this note, we treat vertices in the lattice as Young diagrams and identify maximal chains as certain tableaux. For each i ź - 1 , we define C i ( n ) as the set of maximal chains in T n of length n + i . We give a recursion for # C i ( n ) and an explicit formula based on predetermined initial values. The formula is a polynomial in n of degree 3 i + 3 . For example, the number of maximal chains of length n in T n is # C 0 ( n ) = n 3 . The formula has a combinatorial interpretation in terms of a special property of maximal chains. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.disc.2016.11.030 | Discrete Mathematics |
Keywords | Field | DocType |
Tamari lattice,Number of maximal chains,Enumeration,Recursion,Tableaux | Tamari lattice,Discrete mathematics,Combinatorics,Lattice (order),Polynomial,Vertex (geometry),Enumeration,Mathematics,Recursion | Journal |
Volume | Issue | ISSN |
340 | 4 | Discrete Math. 340 (2017), no. 4, 661--677. MR3603545 |
Citations | PageRank | References |
0 | 0.34 | 5 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Luke Nelson | 1 | 0 | 0.34 |