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Nandor Sieben

Publications and source records attributed to Nandor Sieben.

27 records · Page 2Linked to original sources
arXiv2010

Bounds on the Rubbling and Optimal Rubbling Numbers of Graphs

A pebbling move on a graph removes two pebbles at a vertex and adds one pebble at an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed. In this new move, one pebble each is removed at vertices $v$ and $w$ adjacent to a vertex $u$, and an extra pebble is added at vertex $u$. A vertex is reachable from a pebble distribution if it is possible to move a pebble to that vertex using rubbling moves. The rubbling number is the smallest number $m$ needed to guarantee that any vertex is reachable from any pebble distribution of $m$ pebbles. The optimal rubbling number is the smallest number $m$ needed to guarantee a pebble distribution of $m$ pebbles from which any vertex is reachable. We give bounds for rubbling and optimal rubbling numbers. In particular, we find an upper bound for the rubbling number of $n$-vertex, diameter $d$ graphs, and estimates for the maximum rubbling number of diameter 2 graphs. We also give a sharp upper bound for the optimal rubbling number, and sharp upper and lower bounds in terms of the diameter.

math.CO↗
arXiv2010

Critical branching random walk in an IID environment

Using a high performance computer cluster, we run simulations regarding an open problem about d-dimensional critical branching random walks in a random IID environment The environment is given by the rule that at every site independently, with probability p>0, there is a cookie, completely suppressing the branching of any particle located there. Abstract. The simulations suggest self averaging: the asymptotic survival probability in n steps is the same in the annealed and the quenched case; it is \frac{2}{qn}, where q:=1-p. This particular asymptotics indicates a non-trivial phenomenon: the tail of the survival probability (both in the annealed and the quenched case) is the same as in the case of non-spatial unit time critical branching, where the branching rule is modified: branching only takes place with probability q for every particle at every iteration.

math.PR↗
arXiv2009

A graph pebbling algorithm on weighted graphs

A pebbling move on a weighted graph removes some pebbles at a vertex and adds one pebble at an adjacent vertex. The number of pebbles removed is the weight of the edge connecting the vertices. A vertex is reachable from a pebble distribution if it is possible to move a pebble to that vertex using pebbling moves. The pebbling number of a weighted graph is the smallest number $m$ needed to guarantee that any vertex is reachable from any pebble distribution of $m$ pebbles. Regular pebbling problems on unweighted graphs are special cases when the weight on every edge is 2. A regular pebbling problem often simplifies to a pebbling problem on a simpler weighted graph. We present an algorithm to find the pebbling number of weighted graphs. We use this algorithm together with graph simplifications to find the regular pebbling number of all connected graphs with at most nine vertices.

math.CO↗
arXiv2007

Rubbling and Optimal Rubbling of Graphs

A pebbling move on a graph removes two pebbles at a vertex and adds one pebble at an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed. In this new move one pebble is removed at vertices v and w adjacent to a vertex u and an extra pebble is added at vertex u. A vertex is reachable from a pebble distribution if it is possible to move a pebble to that vertex using rubbling moves. The rubbling number of a graph is the smallest number m needed to guarantee that any vertex is reachable from any pebble distribution of m pebbles. The optimal rubbling number is the smallest number m needed to guarantee a pebble distribution of m pebbles from which any vertex is reachable. We determine the rubbling and optimal rubbling number of some families of graphs including cycles.

math.CO↗
arXiv2007

Avoidable Sets in The Bicyclic Inverse Semigroup

A subset $U$ of a set $S$ with a binary operation is called {\it avoidable} if $S$ can be partitioned into two subsets $A$ and $B$ such that no element of $U$ can be written as a product of two distinct elements of $A$ or as the product of two distinct elements of $B$. The avoidable sets of the bicyclic inverse semigroup are classified.

math.CO↗
arXiv1999

A Note on Primitive Equivalence

Primitive equivalence of graphs and matrices was used by Enomoto, Fujii and Watatani to classify Cuntz-Krieger algebras of 3x3 irreducible matrices. In this paper it is shown that the definition of primitive equivalence can be simplified using primitive transfers of matrices that involve only two rows of the matrix.

math.FA↗
arXiv1997

C*-Crossed Products by Twisted Inverse Semigroup Actions

The notions of Busby-Smith and Green type twisted actions are extended to discrete unital inverse semigroups. The connection between the two types, and the connection with twisted partial actions, are investigated. Decomposition theorems for the twisted crossed products are given.

funct-an↗
arXiv1996

C*-crossed products by partial actions and actions of inverse semigroups

The recently developed theory of partial actions of discrete groups on $C^*$-algebras is extended. A related concept of actions of inverse semigroups on $C^*$-algebras is defined, including covariant representations and crossed products. The main result is that every partial crossed product is a crossed product by a semigroup action.

funct-an↗