Quasi-Differential Posets and Cover Functions of Distributive Lattices II: A Problem in Stanley's Enumerative Combinatorics
نویسنده
چکیده
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 ðnÞ 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.
منابع مشابه
Distributive lattices of small width, II: A problem from Stanley's 1986 text Enumerative Combinatorics
Article history: Received 11 December 2006 Available online 16 April 2009
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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. In this paper, all finitary distributive lattices with non-decreasing cover functions are characterized. A 1975 conjecture of Richard P. Stanley is thereby settled. 2000 Academic Press
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ورودعنوان ژورنال:
- Graphs and Combinatorics
دوره 19 شماره
صفحات -
تاریخ انتشار 2003