Annals of Combinatorics 8 (2004) 37-43

Edward Early

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
efedula@math.mit.edu

Received September 7, 2003

AMS Subject Classification: 06A07

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

Keywords: chain lengths, posets, Tamari lattice

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

2.  A. Bj¨orner 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.

Get the DVI | PS | PDF file of this abstract.