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SUBBUNDLES OF MAXIMAL DEGREE
, 2003
"... Let C be a curve of genus g and E a generic (semistable) vector bundle of rank r and degree d. Fix a rank r ′ < r and a degree d ′ for subsheaves E ′ of E. If r ′ d −rd ′ = r ′ (r −r ′)(g − 1), the number of such subbundles is finite. We shall denote this number with m(r, d, r ′ , g). ..."
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Cited by 2 (0 self)
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Let C be a curve of genus g and E a generic (semistable) vector bundle of rank r and degree d. Fix a rank r ′ < r and a degree d ′ for subsheaves E ′ of E. If r ′ d −rd ′ = r ′ (r −r ′)(g − 1), the number of such subbundles is finite. We shall denote this number with m(r, d, r ′ , g).
Maximizing degrees of freedom in wireless networks
 in Proceedings of 40th Annual Allerton Conference on Communication, Control and Computing
, 2003
"... in Electrical Engineering and Computer Science We consider communication from a single source to a single destination in a wireless network with fading. Both source and destination have multiple antennas. The information reaches the destination through a sequence of layers of singleantenna relays. ..."
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Cited by 11 (0 self)
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in Electrical Engineering and Computer Science We consider communication from a single source to a single destination in a wireless network with fading. Both source and destination have multiple antennas. The information reaches the destination through a sequence of layers of singleantenna relays. A nonseparationbased strategy is proposed and shown to achieve a rate equal to the capacity of a pointtopoint multiantenna system in the high SNR regime. This implies that lack of coordination between relay nodes does not reduce the achievable rate at high SNR. We then derive the tradeoffs between network size and rate. We also derive the ratediversity tradeoff for this network and study how it is affected by the network size. This shows that increasing network size is much more difficult when the codelength does not span a large number of fading realizations. Finally
Maximizing the Spread of Influence Through a Social Network
 In KDD
, 2003
"... Models for the processes by which ideas and influence propagate through a social network have been studied in a number of domains, including the diffusion of medical and technological innovations, the sudden and widespread adoption of various strategies in gametheoretic settings, and the effects of ..."
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Cited by 990 (7 self)
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perform nodeselection heuristics based on the wellstudied notions of degree centrality and distance centrality from the field of social networks.
Maximal degree in the Strong Bruhat Order of Bn
, 2006
"... Given a permutation π ∈ Sn, let Γ−(π) be the graph on n vertices {1,..., n} where two vertices i < j are adjacent if π −1 (i)> π −1 (j) and there are no integers k, i < k < j, such that π −1 (i)> π −1 (k)> π −1 (j). Let Γ(π) be the graph obtained by dropping the condition that π −1 ..."
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Given a permutation π ∈ Sn, let Γ−(π) be the graph on n vertices {1,..., n} where two vertices i < j are adjacent if π −1 (i)> π −1 (j) and there are no integers k, i < k < j, such that π −1 (i)> π −1 (k)> π −1 (j). Let Γ(π) be the graph obtained by dropping the condition that π −1 (i)> π −1 (j), i.e. two vertices are adjacent if the rectangle [i, π(i)] × [j, π(j)] is empty. In the study of the strong order on permutation, Adin and Roichman introduced these graphs and computed their maximum number of edges. We generalize these results to the Weyl group of signed permutations Bn, working with graphs on vertices {−n,...,n} \ {0}, using new variants of a classical theorem of Turán. 1
Minimal Size Of A Graph With Diameter 2 And Given Maximal Degree, II
, 1992
"... Let F 2 (n; bpnc) be the minimal size of a graph on n vertices with diameter 2 and maximal degree bpnc. The asymptotic behaviour of F 2 (n; bpnc) is considered for 2=5 ! p ! 5=12. ..."
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Let F 2 (n; bpnc) be the minimal size of a graph on n vertices with diameter 2 and maximal degree bpnc. The asymptotic behaviour of F 2 (n; bpnc) is considered for 2=5 ! p ! 5=12.
Enumerating Permutation Polynomials I: Permutations with NonMaximal Degree
, 2002
"... s can be found in the book of Lidl and Niederreiter [5]. Various applications of permutation polynomials to cryptography have been described. See for example [1,2]. Lidl and Mullen in [3,4] (see also [6]) describe a number of open problems regarding permutations polynomials: among these, the problem ..."
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Cited by 3 (2 self)
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, the problem of enumerating permutation polynomials by their degree. We denote by S s fx 2 F sx=xg the set of those elements of F q which are moved by s. Our first remark is that @f s #q#j if s=id: 2 T see this it is enough to note that the polynomial f s x#x has as roots all the elements of F q fixed
Corrigendum Corrigendum to “enumerating permutation polynomials—I: Permutations with nonmaximal degree”
, 2005
"... Let Fq be a finite field with q elements and suppose C is a conjugation class of permutations of the elements of Fq. We denote by C = (c1; c2;...; ct) the conjugation class of permutations that admit a cycle decomposition with ci icycles (i = 1,...,t). Further, we set c = 2c2 +···+tct = q − c1 to b ..."
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Let Fq be a finite field with q elements and suppose C is a conjugation class of permutations of the elements of Fq. We denote by C = (c1; c2;...; ct) the conjugation class of permutations that admit a cycle decomposition with ci icycles (i = 1,...,t). Further, we set c = 2c2 +···+tct = q − c1 to be the number of elements of Fq moved by any permutation in C. If � ∈ C, then the permutation polynomial associated to � is defined as f�(t) = � Therefore for q>3 the function x∈Fq �(x) 1 − (t − x) q−1�
Results 1  10
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4,306