منابع مشابه
Geometric Applications Of Posets
We show the power of posets in computational geometry by solving several problems posed on a set S of n points in the plane: (1) nd the n ? k ? 1 rectilinear farthest neighbors (or, equivalently, k nearest neighbors) to every point of S (extendable to higher dimensions), (2) enumerate the k largest (smallest) rectilinear distances in decreasing (increasing) order among the points of S, (3) give...
متن کاملWord posets, with applications to Coxeter groups
We discuss the theory of certain partially ordered sets that capture the structure of commutation classes of words in monoids. As a first application, it follows readily that counting words in commutation classes is #P-complete. We then apply the partially ordered sets to Coxeter groups. Some results are a proof that enumerating the reduced words of elements of Coxeter groups is #P-complete, a ...
متن کاملBruhat order on plane posets and applications
A plane poset is a finite set with two partial orders, satisfying a certain incompatibility condition. The set PP of isoclasses of plane posets owns two products, and an infinitesimal Hopf algebra structure is defined on the vector space HPP generated by PP , using the notion of biideals of plane posets. We here define a partial order on PP , making it isomorphic to the set of partitions with t...
متن کاملFactorization of the Characteristic Polynomial of a Lattice using Quotient Posets
We introduce a new method for showing that the roots of the characteristic polynomial of a finite lattice are all nonnegative integers. Our method gives two simple conditions under which the characteristic polynomial factors. We will see that Stanley’s Supersolvability Theorem is a corollary of this result. We can also use this method to demonstrate a new result in graph theory and give new pro...
متن کاملEquivariant Homotopy of Posets and Some Applications to Subgroup Lattices
In this paper we consider the action of a finite group G on the geometric realization ]CP[ of the order complex CP of a poset P, on which a group G acts as a group of poset automorphisms. For special cases we give the G-homotopy type of ]CPr. Moreover, we provide conditions which imply that the orbit space I CPI/G is homotopy equivalent to the geometric realization of the order complex over the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2017
ISSN: 0012-365X
DOI: 10.1016/j.disc.2016.11.019