THE MINIMUM-WEIGHT IDEAL PROBLEM FOR SIGNED POSETS

The Minimum-weight Ideal Problem for Signed Posets

The concept of signed poset has recently been introduced by V. Reiner as a generalization of that of ordinary poset (partially ordered set). We consider the problem of finding a minimum-weight ideal of a signed poset. We show a representation theorem that there exists a bijection between the set of all the ideals of a signed poset and the set of all the "reduced ideals" (defined here) of the as...

Signed Posets

We define a new object, called a signed poset, that bears the same relation to the hyperoctahedral group B n (i.e., signed permutations on n letters), as do posets to the symmetric group S n. We then prove hyperoctahedral analogues of the following results: (1) the generating function results from the theory of P-partitions; (2) the fundamental theorem of finite distributive lattices (or Birkho...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

An Efficient Algorithm for the Minimum-range Ideal Problem

Suppose we are given a partially ordered set, a real-valued weight associated with each element and a positive integer k. We consider the problem which asks to find an ideal of size k of the partially ordered set such that the range of the weights is minimum. We call this problem the minimum-range ideal problem. This paper shows a new and fast 0 ( n log n + m) algorithm for this problem, where ...

Upper Binomial Posets and Signed Permutation Statistics