Chain Lengths in the Tamari Lattice

Edward Early

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

efedula@math.mit.edu

Annals of Combinatorics 8 (1) p.37-43 March, 2004

Abstract:

We find the size of the largest union of two or three chains in the Tamari lattice.

References:

1. M.K. Bennett and G. Birkhoff, Two families of Newman lattices, Algebra Universalis 32 (1994) 115–144.

2. A. Björner and M.L.Wachs, Shellable nonpure complexes and posets II, Trans. Amer. Math. Soc. 349 (1997) 3945–3975.

3. A. Blass and B.E. Sagan, Möbius functions of lattices, Adv. Math. 127 (1997) 94–123.

4. T. Britz and S. Fomin, Finite posets and Ferrers shapes, Adv. Math. 158 (2001) 86–127.

5. W. Geyer, On Tamari lattices, Discrete Math. 133 (1994) 99–122.

6. C. Greene, Some partitions associated with a partially ordered set, J. Combin. Theory, Ser. A 20 (1976) 69–79.

7. C. Greene and D.J. Kleitman, The structure of Sperner k-families, J. Combin. Theory, Ser. A 20 (1976) 41–68.

8. S. Huang and D. Tamari, Problems of associativity: a simple proof for the lattice property of systems ordered by a semi-associative law, J. Combin. Theory, Ser. A 13 (1972) 7–13.

9. G. Markowsky, Primes, irreducibles and extremal lattices, Order 9 (1992) 265–290.