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Ordered Partitions Avoiding a Permutation Pattern of Length 3
pattern avoidance ordered partition descent
2014/6/3
An ordered partition of [n]={1, 2,..., n} is a partition whose blocks are endowed with a linear order. Let OPn,k be set of ordered partitions of [n] with k blocks and OPn,k(σ) be set of ordered partit...
Ordering subsets of (partially) ordered sets: Representation theorems
partial orders ordering subsets of a poset
2010/9/20
In many practical situations, we have a (partially) ordered set V of different values. For example, we may have the set of all possible values of temperature, or the set of all possible degrees of con...
On the ordered sets in n-dimensional real inner product spaces
Real inner product space Lorentz-Minkowski distance Lorentz trans-formation
2008/12/26
Let X be a real inner product space of dimension ¸ 2. In [2],
W. Benz proved the following theorem for x; y 2 X with x < y: "The
Lorentz-Minkowski distance between x and y is zero (i.e., l (x;...
On Jensen Type Inequalities With Ordered Variables
Convex function $k$-arithmetic ordered variables $k$-geometric ordered variables Jensen's inequality Karamata's inequality
2008/6/27
In this paper, we present some basic results concerning an extension of Jensen type inequalities with ordered variables to functions with inflection points, and then give several relevant applications...
A Combinatorial Theorem on Ordered Circular Sequences of n_1 u's and n_2 v' s with Application to Kernel-perfect Graphs
ordered circular sequences kernel kernel-perfect
2007/12/11
1 or δ = 0 for d = 1, and n,d,r,s are positive integers with (n,d) = r and n = mr, and gave some necessary and sufficient conditions for G(n,d,r,s) with r ≥ 3 and s = 1 to be KP or KPC. In this paper,...
A graph g is k-ordered Hamiltonian, 2 ≤ k ≤ n, if for every ordered sequence S of k distinct vertices of G, there exists a Hamiltonian cycle that encounters S in the given order. In this article, we p...