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Cogrowth of Arbitrary Graphs
"... Abstract. A “cogrowth set ” of a graph G is the set of vertices in the universal cover of G which are mapped by the universal covering map onto a given vertex of G. Roughly speaking, a cogrowth set is large if and only if G is small. In particular, when G is regular, a cogrowth constant (a measure o ..."
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graph. This proof is based on some properties of a family of Laplacians related to the zeta function of the covered graph. An example is given where this result fails when G does not cover a finite graph. Second, for any graph with transient covering tree, we define a new cogrowth constant expressed
On the cogrowth of Thompson’s group
 F . Groups Complex. Cryptol
"... We investigate the cogrowth and distribution of geodesics in R. Thompson’s group F. 1 ..."
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Cited by 5 (3 self)
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We investigate the cogrowth and distribution of geodesics in R. Thompson’s group F. 1
Nonbacktracking random walks and cogrowth of graphs
 Canadian Journal of Mathematics
"... Abstract. Let X be a locally finite, connected graph without vertices of degree 1. Nonbacktracking random walk moves at each step with equal probability to one of the “forward ” neighbours of the actual state, i.e., it does not go back along the preceding edge to the preceding state. This is not a ..."
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Cited by 16 (1 self)
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concerning cogrowth of groups, and makes the extension of that result to arbitrary regular graphs rigorous. Even when X is nonregular, but small cycles are dense in X, we show that the graph X is nonamenable if and only if the nonbacktracking nstep transition probabilities decay exponentially fast
On the cogrowth of Thompson’s group F 1
"... We investigate the cogrowth and distribution of geodesics in R. Thompson’s group F. ..."
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We investigate the cogrowth and distribution of geodesics in R. Thompson’s group F.
A Short Proof of the GrigorchukCohen Cogrowth Theorem
 Proc. Amer. Math. Soc
, 1989
"... ABSTRACT. Let G be a group generated by gl,...,gr. There are exactly 2r(2r l)n1 reduced words in gl,..,gr of length n. Part of them, say Yn represents identity element of G. Let y = limsupyn. We give a short proof of the theorem of Grigorchuk and Cohen which states that G is amenable if and only i ..."
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Cited by 9 (1 self)
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if y = 2r 12. Moreover we derive some new properties of the generating function E Yn zn Let G be a finitely generated discrete group. Consider G as an epimorphic image it: Fr G of the free group Fr on r generators. Thus G is isomorphic to the quotient group Fr/N where N = ker X is a normal subgroup
The
"... ratio and generating function of cogrowth coefficients of finitely generated groups ..."
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ratio and generating function of cogrowth coefficients of finitely generated groups
The
, 711
"... ratio and generating function of cogrowth coefficients of finitely generated groups ..."
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ratio and generating function of cogrowth coefficients of finitely generated groups
ON TRIVIAL WORDS IN FINITELY PRESENTED GROUPS
"... all great men of generating functions. Abstract. We propose a numerical method for studying the cogrowth of finitely presented groups. To validate our numerical results we compare them against the corresponding data from groups whose cogrowth series are known exactly. Further, we add to the set of s ..."
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all great men of generating functions. Abstract. We propose a numerical method for studying the cogrowth of finitely presented groups. To validate our numerical results we compare them against the corresponding data from groups whose cogrowth series are known exactly. Further, we add to the set
Thinking On Building New Managerial Theory
"... The paper puts forward a new managerial thought and theory including 12 points which absorbs and integrates the essence of oriental and occidental counterparts. It advocates that sustainable development be the principle that must be adhered to attain the cogrowth of the human, the society and natur ..."
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The paper puts forward a new managerial thought and theory including 12 points which absorbs and integrates the essence of oriental and occidental counterparts. It advocates that sustainable development be the principle that must be adhered to attain the cogrowth of the human, the society
Genericcase complexity and decision problems in group theory, preprint
, 2003
"... Abstract. We give a precise definition of “genericcase complexity” and show that for a very large class of finitely generated groups the classical decision problems of group theory the word, conjugacy and membership problems all have lineartime genericcase complexity. We prove such theorems by ..."
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Cited by 69 (26 self)
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Abstract. We give a precise definition of “genericcase complexity” and show that for a very large class of finitely generated groups the classical decision problems of group theory the word, conjugacy and membership problems all have lineartime genericcase complexity. We prove such theorems by using the theory of random walks on regular graphs. Contents 1. Motivation
Results 1  10
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