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![Figure 1: A recursive tree on [10].](https://thumb-ap.123doks.com/thumbv2/123dok/975543.914751/3.612.188.389.414.567/figure-a-recursive-tree-on.webp)
![Figure 2: The cutting procedure for a random recursive tree on [10], with the cuts indicated.](https://thumb-ap.123doks.com/thumbv2/123dok/975543.914751/5.612.82.496.211.599/figure-cutting-procedure-random-recursive-tree-cuts-indicated.webp)
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Since we process the candidate faces from left to right and the vertices in a face from right to left, only the rightmost vertex of a path in a leftist ordered path partition can
A notion of additive dilogarithm for a field k is intro- duced, based on the K-theory and higher Chow groups of the affine line relative to 2(0).. Analogues of the K 2 -regulator,
Hence if we assume that only one vertex of the chosen edge is covered, then the modified process is just the classical coupon collector’s problem, and therefore its mean cover time N
In section 5, we study the integrability of the Green function of the walk which ensures the existence of the original (non killed) Kalikow’s auxiliary walk and finish the proof of
One example of a graph model for obtaining a prescribed degree distribution is the so called configuration model – see Molloy and Reed (1995,1998) – where, given n vertices, each
We define the ERW on a tree G as the process which goes toward the root with probability 1 − ε when it visits a vertex v for the first time and goes to every neighbor of v with
Finally, we note that the proof of the convergence (3) of Theorem 2 (which is given in Section 4) works as it is, when we start the Markov chain with a translation invariant
We present the trigonometric Lax matrix and classical r -matrix for the Kowa- levski gyrostat on so (4) algebra by using the auxiliary matrix algebras so (3 , 2) or sp (4).. Key
