Let L be a recursive algebraic extension of Q. Assume that, given α ∈ L, we can compute the roots in L of its minimal polynomial over Q and we can determine which roots are Aut(L)-conjugate to α. We prove there exists a pair of polynomials that characterizes the Aut(L)-conjugates of α, and that these polynomials can be effectively computed. Assume furthermore that L can be embedded in R, or in ...

Let C be a finite set of n elements and R = {r1, r2, . . . , rm} a family of m subsets of C. A subset X of R verifies the Consecutive Ones Property (C1P) if there exists a permutation P of C such that each ri in X is an interval of P . A Minimal Conflicting Set (MCS) S ⊆ R is a subset of R that does not verify the C1P, but such that any of its proper subsets does. In this paper, we present a ne...

A minimal k-cycle is a family of sets A0, . . . , Ak−1 for which Ai ∩Aj 6= ∅ if and only if i = j or i and j are consecutive modulo k. Let fr(n, k) be the maximum size of a family of r-sets of an n element set containing no minimal k-cycle. Our results imply that for fixed r, k ≥ 3, ` ( n− 1 r − 1 ) +O(nr−2) ≤ fr(n, k) ≤ 3` ( n− 1 r − 1 ) +O(nr−2), where ` = b(k− 1)/2c. We also prove that fr(n,...

we define minimal cn-dominating graph $mathbf {mcn}(g)$, commonality minimal cn-dominating graph $mathbf {cmcn}(g)$ and vertex minimal cn-dominating graph $mathbf {m_{v}cn}(g)$, characterizations are given for graph $g$ for which the newly defined graphs are connected. further serval new results are developed relating to these graphs.

We prove that in almost all large tournaments, the minimal covering set is the entire set of alternatives. That is, as the number of alternatives gets large, the probability that the minimal covering set of a uniformly chosen random tournament is the entire set of alternatives goes to one. By contrast, it follows from a result of Fisher and Reeves (1995) that the bipartisan set contains about h...

In this paper, we consider an approximation of the ordering cone by a sequence of convex well-based cones that are contained inside the original cone. We derive related results on approximating minimal point sequences and propose a density result being evocative of the well-known ABB theorem.