Quasi-Differential Posets and Cover Functions of Distributive Lattices: I. A Conjecture of Stanley
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 (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
منابع مشابه
Quasi-Differential Posets and Cover Functions of Distributive Lattices II: A Problem in Stanley's Enumerative Combinatorics
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 character...
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 90 شماره
صفحات -
تاریخ انتشار 2000