In this paper, we show that if a partially ordered set has 2n elements and has dimension n, then it is isosnorphic to the set of n-l element subsets and lelement subsets of a sef, ordered by inclusion, or else it has six elements and is isomorphic to a partially ordered b;i we call the chevron or to its dual.

Mergers are thought to be a fundamental channel for galaxy growth, perturbing the gas dynamics and magnetic fields (B-fields) in interstellar medium (ISM). However, mechanisms that amplify dissipate B-fields during merger remain unclear. We characterize morphology of ordered multi-phase ISM closest two spiral galaxies, Antennae galaxies. compare inferred using $154~\mu$m thermal dust $11$ cm ra...

which reduce to (n + 1) for a = b = c = 1. We refine Cayley’s formula by showing that Pn(a, b, c) counts rooted forests by the number of trees and the number of proper vertices, which are vertices that are less than all of their proper descendants. Moreover, other evaluations of Pn(a, b, c) have similar interpretations for other types of trees and forests: k-ary trees, forests of ordered trees,...

An inequality between the number of coverings in the ordered set J(Con L) of join irreducible congruences on a lattice L and the size of L is given. Using this inequality it is shown that this ordered set can be computed in time O(n2 log2 n), where n = |L|. This paper is motivated by the problem of efficiently calculating and representing the congruence lattice Con L of a finite lattice L. Of c...

If M and Nare ordered groups, we denote by Mx N the group MxNequipped with the lexicographical order: (a,b) < (a',b') if and only if a < a' or {a = a' and b < b'). In [1], A. L. S. Corner gives an example of two countable abelian groups A, G such that G and A x A x G are isomorphic while G and A x G are not isomorphic; he also gives an example of two nonisomorphic countable abelian groups G, H ...

The notation "" for OR is bad and misleading. Just think that in the context of boolean functions, the author uses  instead of ∨.The integers modulo 2, that is Z2  0,1, have an addition where 1  1  0 while 1 ∨ 1  1. A set A is partially ordered by a binary relation ≤, if this relation is reflexive, that is a ≤ a holds for every element a ∈ S, it is transitive, that is if a ≤ b and b ≤ c...