Skip to main content
SpringerLink
Log in

Quasi-Differential Posets and Cover Functions of Distributive Lattices II: A Problem in Stanley’s Enumerative Combinatorics

  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

A distributive lattice L with 0 is finitary if every interval is finite. A function f:ℕ0→ℕ0 is a cover function for L if every element with n lower covers has f(n) upper covers. All non-decreasing cover functions have been characterized by the author ([2]), settling a 1975 conjecture of Richard P. Stanley. In this paper, all finitary distributive lattices with cover functions are characterized. A problem in Stanley’s Enumerative Combinatorics is thus solved.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Jonathan David Farley

Authors
  1. Jonathan David Farley
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

2000 Mathematics Subject Classification. 06A07, 06B05, 06D99, 11B39

Rights and permissions

Reprints and permissions

About this article

Cite this article

Farley, J. Quasi-Differential Posets and Cover Functions of Distributive Lattices II: A Problem in Stanley’s Enumerative Combinatorics . Graphs and Combinatorics 19, 475–491 (2003). https://doi.org/10.1007/s00373-003-0525-0

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-003-0525-0

Keywords

Search

Navigation