Generating random elements of finite distributive lattices
نویسنده
چکیده
This survey article describes a method for choosing uniformly at random from any finite set whose objects can be viewed as constituting a distributive lattice. The method is based on ideas of the author and David Wilson for using “coupling from the past” to remove initialization bias from Monte Carlo randomization. The article describes several applications to specific kinds of combinatorial objects such as tilings, constrained lattice paths, and alternating-sign matrices. This article is dedicated to Herbert Wilf in honor of his sixty-fifth birthday.
منابع مشابه
Distributive lattices with strong endomorphism kernel property as direct sums
Unbounded distributive lattices which have strong endomorphism kernel property (SEKP) introduced by Blyth and Silva in [3] were fully characterized in [11] using Priestley duality (see Theorem 2.8}). We shall determine the structure of special elements (which are introduced after Theorem 2.8 under the name strong elements) and show that these lattices can be considered as a direct product of ...
متن کاملFUZZY ORDERED SETS AND DUALITY FOR FINITE FUZZY DISTRIBUTIVE LATTICES
The starting point of this paper is given by Priestley’s papers, where a theory of representation of distributive lattices is presented. The purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. In this way, some results of Priestley’s papers are extended. In the main theorem, we show that the category of finite fuzzy Priestley space...
متن کاملFinite distributive lattices are congruence lattices of almost- geometric lattices
A semimodular lattice L of finite length will be called an almost-geometric lattice, if the order J(L) of its nonzero join-irreducible elements is a cardinal sum of at most two-element chains. We prove that each finite distributive lattice is isomorphic to the lattice of congruences of a finite almost-geometric lattice.
متن کاملAn inequality for the sizes of prime filters of finite distributive lattices
Let L be a finite distributive lattice, and let J(L) denote the set of all join-irreducible elements of L. Set j (L) = IJ(Z)l. For each a C J(L), let u(a) denote the number of elements in the prime filter {x C L: x >~a}. Our main theorem is Theorem 1. For any finite distributive lattice L, 4 "(a) ~>j(L)41q ,'2. aEJ(L) The base 4 here can most likely be replaced by a smaller number, but it canno...
متن کاملExponents of Finite Simple Lattices
In the late 1930's Garrett Birkhoff [3] pioneered the theory of distributive lattices. An important component in this theory is the concept of exponentiation of lattices [4]: for a lattice L and a partially ordered set P let L denote the set of all order-preserving maps of P to L partially ordered b y / ^ g if and only if/(;c) ^ g(x) for each x e P (see Figure 1). Indeed, If is a lattice. This ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electr. J. Comb.
دوره 4 شماره
صفحات -
تاریخ انتشار 1997