منابع مشابه
Unimodular random trees
We consider unimodular random rooted trees (URTs) and invariant forests in Cayley graphs. We show that URTs of bounded degree are the same as the law of the component of the root in an invariant percolation on a regular tree. We use this to give a new proof that URTs are sofic, a result of Elek. We show that ends of invariant forests in the hyperbolic plane converge to ideal boundary points. We...
متن کاملThe Ramsey numbers of large trees versus wheels
For two given graphs G1 and G2, the Ramseynumber R(G1,G2) is the smallest integer n such that for anygraph G of order n, either $G$ contains G1 or the complementof G contains G2. Let Tn denote a tree of order n andWm a wheel of order m+1. To the best of our knowledge, only R(Tn,Wm) with small wheels are known.In this paper, we show that R(Tn,Wm)=3n-2 for odd m with n>756m^{10}.
متن کاملEssential Kurepa Trees versus Essential Jech-Kunen Trees
By an !1{tree we mean a tree of cardinality !1 and height !1. An !1{tree is called a Kurepa tree if all its levels are countable and it has more than !1 branches. An !1{tree is called a Jech{Kunen tree if it has branches for some strictly between !1 and 2 1. A Kurepa tree is called an essential Kurepa tree if it contains no Jech{Kunen subtrees. A Jech{Kunen tree is called an essential Jech{Kune...
متن کاملSpace versus Time: Unimodular versus Non-Unimodular Projective Ring Geometries?
Finite projective (lattice) geometries defined over rings instead of fields have recently been recognized to be of great importance for quantum information theory. We believe that there is much more potential hidden in these geometries to be unleashed for physics. There exist specific rings over which the projective spaces feature two principally distinct kinds of basic constituents (points and...
متن کاملOne-Sided Interval Trees
We give an alternative treatment and extension of some results of Itoh and Mahmoud on one-sided interval trees. The proofs are based on renewal theory, including a case with mixed multiplicative and additive renewals.
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ژورنال
عنوان ژورنال: The European Physical Journal C
سال: 2016
ISSN: 1434-6044,1434-6052
DOI: 10.1140/epjc/s10052-016-4384-2