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Combinatorics of geometrically distributed random variables: Lefttoright maxima
 Discrete Mathematics
, 1996
"... Abstract. For words of length n, generated by independent geometric random variables, we consider the mean and variance of the number of inversions and of a parameter of Knuth from permutation in situ. In this way, q–analogues for these parameters from the usual permutation model are obtained. 1. ..."
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Cited by 39 (9 self)
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Abstract. For words of length n, generated by independent geometric random variables, we consider the mean and variance of the number of inversions and of a parameter of Knuth from permutation in situ. In this way, q–analogues for these parameters from the usual permutation model are obtained. 1.
The number of distinct values of some multiplicity in sequences of geometrically distributed . . .
"... ..."
Combinatorics of Geometrically Distributed Random Variables: Value and Position of the rth LefttoRight Maximum
 Discrete Math
"... For words of length n, generated by independent geometric random variables, we consider the average value and the average position of the rth lefttoright maximum, for fixed r and n !1. 1. ..."
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Cited by 8 (5 self)
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For words of length n, generated by independent geometric random variables, we consider the average value and the average position of the rth lefttoright maximum, for fixed r and n !1. 1.
The Number of Distinct Values in a Geometrically Distributed Sample
"... For words of length n, generated by independent geometric random variables, we consider the average and variance of the number of distinct values (= letters) that occur in the word. We then generalise this to the number of values which occur at least b times in the word. 1. ..."
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Cited by 8 (2 self)
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For words of length n, generated by independent geometric random variables, we consider the average and variance of the number of distinct values (= letters) that occur in the word. We then generalise this to the number of values which occur at least b times in the word. 1.
Reliability benefit of network coding
, 2007
"... The capacity benefit of network coding has been extensively studied in wired and wireless networks. Moreover, it has been shown that network coding improves network reliability by reducing the number of packet retransmissions in lossy networks. However, the extent of the reliability benefit of netwo ..."
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Cited by 7 (1 self)
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The capacity benefit of network coding has been extensively studied in wired and wireless networks. Moreover, it has been shown that network coding improves network reliability by reducing the number of packet retransmissions in lossy networks. However, the extent of the reliability benefit of network coding is not known. In this work, we characterize the reliability benefit of network coding for reliable multicasting. In particular, we show that the expected number of transmissions using linkbylink ARQ compared to network coding to send a packet from the multicast source to K receivers scales as Θ( log K log log K).
The first descent in samples of geometric random variables and permutations
"... For words of length n, generated by independent geometric random variables, we study the average initial and end heights of the first strict and weak descents in the word. Higher moments and limiting distributions are also derived. In addition we compute the average initial and end height of the fir ..."
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Cited by 1 (1 self)
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For words of length n, generated by independent geometric random variables, we study the average initial and end heights of the first strict and weak descents in the word. Higher moments and limiting distributions are also derived. In addition we compute the average initial and end height of the first descent for a random permutation of n letters.
THE FIBONACCI KILLER*
, 1993
"... We consider the following stochastic process: Assume that a "player " is hit at any time x with probability/?. However, he dies only after two consecutive hits. We might code this process by 0 and 1, marking a hit, e.g., by a "1". Then the sequences associated with a player can be described ..."
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We consider the following stochastic process: Assume that a "player " is hit at any time x with probability/?. However, he dies only after two consecutive hits. We might code this process by 0 and 1, marking a hit, e.g., by a "1". Then the sequences associated with a player can be described