منابع مشابه
Counting Dihedral and Quaternionic Extensions
We give asymptotic formulas for the number of biquadratic extensions of Q that admit a quadratic extension which is a Galois extension of Q with a prescribed Galois group, for example, with a Galois group isomorphic to the quaternionic group. Our approach is based on a combination of the theory of quadratic equations with some analytic tools such as the Siegel–Walfisz theorem and the double osc...
متن کاملCounting Linear Extensions of a Partial Order
A partially ordered set (P,<) is a set P together with an irreflexive, transitive relation. A linear extension of (P,<) is a relation (P,≺) such that (1) for all a, b ∈ P either a ≺ b or a = b or b ≺ a, and (2) if a < b then a ≺ b; in other words, a total order that preserves the original partial order. We define Λ(P ) as the set of all linear extensions of P , and define N(P ) = |Λ(P )|. Throu...
متن کاملCounting Linear Extensions: Parameterizations by Treewidth
We consider the #P-complete problem of counting the number of linear extensions of a poset (#LE); a fundamental problem in order theory with applications in a variety of distinct areas. In particular, we study the complexity of #LE parameterized by the well-known decompositional parameter treewidth for two natural graphical representations of the input poset, i.e., the cover and the incomparabi...
متن کاملCounting Linear Extensions of Sparse Posets
Counting the linear extensions of a partially ordered set (poset) is a fundamental problem with several applications. We present two exact algorithms that target sparse posets in particular. The first algorithm breaks the counting task into subproblems recursively. The second algorithm uses variable elimination via inclusion–exclusion and runs in polynomial time for posets with a cover graph of...
متن کاملCounting Using Hall Algebras Ii. Extensions from Quivers
We count the Fq-rational points of GIT quotients of quiver representations with relations. We focus on two types of algebras – one is one-point extended from a quiver Q, and the other is the Dynkin A2 tensored with Q. For both, we obtain explicit formulas. We study when they are polynomial-count. We follow the similar line as in the first paper but algebraic manipulations in Hall algebra will b...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1990
ISSN: 0097-3165
DOI: 10.1016/0097-3165(90)90070-d