The number of essentially different square polyominoes of order n and minimum perimeter p(n) is enumerated.

Two natural foliations, guided by area and perimeter, of the configurations spaces planar polygons are considered topology their leaves is investigated in some detail. In particular, homology groups homotopy type determined. The with fixed perimeter also Besides, we extend classical isoperimetric duality to all critical points. conclusion a few general remarks on dual extremal problems polygon ...

From a security standpoint, it is preferable to implement least privilege network security policies in which only the bare minimum of TCP/UDP ports on internal hosts are accessible from outside the perimeter. Unfortunately, organizations with such policies can no longer communicate using common multiport protocols that require randomly chosen ports for auxiliary connections. This paper introduc...

The covariogram of a measurable set A ⊂ R is the function gA which to each y ∈ R associates the Lebesgue measure of A ∩ (y + A). This paper proves two formulas. The first equates the directional derivatives at the origin of gA to the directional variations of A. The second equates the average directional derivative at the origin of gA to the perimeter of A. These formulas, previously known with...

The proofs and applications are based on a Riemannian version of Gromov’s non-squeezing theorem and classical integral geometry. Given a convex surface Σ ⊂ R and a point q in the unit sphere S we denote by UΣ(q) the perimeter of the orthogonal projection of Σ onto a plane perpendicular to q. We obtain a function UΣ on the sphere which is clearly continuous, even, and positive. Let us denote the...