اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدBoundary chromatic polynomial
174
0
0.0
(
0
)
تأليف
Jesper Lykke Jacobsen
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider proper colorings of planar graphs embedded in the annulus, such that vertices on one rim can take Q_s colors, while all remaining vertices can take Q colors. The corresponding chromatic polynomial is related to the partition function of a boundary loop model. Using results for the latter, the phase diagram of the coloring problem (with real Q and Q_s) is inferred, in the limits of two-dimensional or quasi one-dimensional infinite graphs. We find in particular that the special role played by Beraha numbers Q=4 cos^2(pi/n) for the usual chromatic polynomial does not extend to the case Q different from Q_s. The agreement with (scarce) existing numerical results is perfect; further numerical checks are presented here.
قيم البحث
اقرأ أيضاً
The Hall tensor emerges from the study of the Hall effect, an important magnetic effect observed in electric conductors and semiconductors. The Hall tensor is third order and three dimensional, whose first two indices are skew-symmetric. In this pape
r, we investigate the isotropic polynomial invariants of the Hall tensor by connecting it with a second order tensor via the third order Levi-Civita tensor. We propose a minimal isotropic integrity basis with 10 invariants for the Hall tensor. Furthermore, we prove that this minimal integrity basis is also an irreducible isotropic function basis of the Hall tensor.
We introduce a nilpotent group to write a generalized quartic anharmonic oscillator Hamiltonian as a polynomial in the generators of the group. Energy eigenvalues are then seen to depend on the values of the two Casimir operators of the group. This d
ependence exhibits a scaling law which follows from the scaling properties of the group generators. Demanding that the potential give rise to polynomial solutions in a particular Lie algebra element puts constraints on the four potential parameters, leaving only two of them free. For potentials satisfying such constraints at least one of the energy eigenvalues and the corresponding eigenfunctions can be obtained in closed analytic form; examples, beyond those available in the literature, are given. Finally, we find solutions for particles in external electromagnetic fields in terms of these quartic polynomial solutions.
Let G be a combinatorial graph with vertices V and edges E. A proper coloring of G is an assignment of colors to the vertices such that no edge connects two vertices of the same color. These are the colorings considered in the famous Four Color Theor
em. It turns out that the number of proper colorings of G using t colors is a polynomial in t, called the chromatic polynomial of G. This polynomial has many wonderful properties. It also has the surprising habit of appearing in contexts which, a priori, have nothing to do with graph coloring. We will survey three such instances involving acyclic orientations, hyperplane arrangements, and increasing forests. In addition, connections to symmetric functions and algebraic geometry will be mentioned.
We show that the averaged characteristic polynomial and the averaged inverse characteristic polynomial, associated with Hermitian matrices whose elements perform a random walk in the space of complex numbers, satisfy certain partial differential, dif
fusion-like, equations. These equations are valid for matrices of arbitrary size. Their solutions can be given an integral representation that allows for a simple study of their asymptotic behaviors for a broad range of initial conditions.
We propose a solution method for studying relativistic spin-$0$ particles. We adopt the Feshbach-Villars formalism of the Klein-Gordon equation and express the formalism in an integral equation form. The integral equation is represented in the Coulom
b-Sturmian basis. The corresponding Greens operator with Coulomb and linear confinement potential can be calculated as a matrix continued fraction. We consider Coulomb plus short range vector potential for bound and resonant states and linear confining scalar potentials for bound states. The continued fraction is naturally divergent at resonant state energies, but we made it convergent by an appropriate analytic continuation.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
