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40
REPRESENTATIONS OF QUANTUM PERMUTATION ALGEBRAS
, 2009
"... We develop a combinatorial approach to the quantum permutation algebras, as Hopf images of representations of type π: As(n) → B(H). We discuss several general problems, including the commutativity and cocommutativity ones, the existence of tensor product or free wreath product decompositions, and ..."
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Cited by 11 (8 self)
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We develop a combinatorial approach to the quantum permutation algebras, as Hopf images of representations of type π: As(n) → B(H). We discuss several general problems, including the commutativity and cocommutativity ones, the existence of tensor product or free wreath product decompositions, and the Tannakian aspects of the construction. The main motivation comes from the quantum invariants of the complex Hadamard matrices: we show here that, under suitable regularity assumptions, the computations can be performed up to n = 6.
and roughly weighted simple games
 Mathematical Social Sciences 61
, 2011
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ON ORTHOGONAL MATRICES MAXIMIZING THE 1NORM
, 901
"... Abstract. For U ∈ O(N) we have U1 ≤ N √ N, with equality if and only if U = H / √ N, with H Hadamard matrix. Motivated by this remark, we discuss in this paper the algebraic and analytic aspects of the computation of the maximum of the 1norm on O(N). The main problem is to compute the kth mom ..."
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Cited by 9 (9 self)
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Abstract. For U ∈ O(N) we have U1 ≤ N √ N, with equality if and only if U = H / √ N, with H Hadamard matrix. Motivated by this remark, we discuss in this paper the algebraic and analytic aspects of the computation of the maximum of the 1norm on O(N). The main problem is to compute the kth moment of the 1norm, with k → ∞, and we present a number of general comments in this direction.
Symmetric Bushtype Hadamard matrices of order 4m^4 exist for all odd m
 PROC. AMER. MATH. SOC
, 2006
"... Using reversible Hadamard difference sets, we construct symmetric Bushtype Hadamard matrices of order 4m^4 for all odd integers m. ..."
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Cited by 7 (2 self)
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Using reversible Hadamard difference sets, we construct symmetric Bushtype Hadamard matrices of order 4m^4 for all odd integers m.
On the classification of Hadamard matrices of order 32
, 2009
"... All equivalence classes of Hadamard matrices of order at most 28 have been found by 1994. Order 32 is where a combinatorial explosion occurs on the number of inequivalent Hadamard matrices. We find all equivalence classes of Hadamard matrices of order 32 which are of certain types. It turns out that ..."
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Cited by 6 (1 self)
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All equivalence classes of Hadamard matrices of order at most 28 have been found by 1994. Order 32 is where a combinatorial explosion occurs on the number of inequivalent Hadamard matrices. We find all equivalence classes of Hadamard matrices of order 32 which are of certain types. It turns out that there are exactly 13,680,757 Hadamard matrices of one type and 26,369 such matrices of another type. Based on experience with the classification of Hadamard matrices of smaller order, it is expected that the number of the remaining two types of these matrices, relative to the total number of Hadamard matrices of order 32, to be insignificant.
The hypergroup property and representation of Markov kernels
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On the real unbiased Hadamard matrices
, 2010
"... The class of mutually unbiased Hadamard (MUH) matrices is studied. We show that the number of MUH matrices of order 4n 2, n odd is at most 2 and that the bound is attained for n = 1,3. Furthermore, we find a lower bound for the number of MUH matrices of order 16n 2, assuming the existence of a Hadam ..."
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Cited by 4 (1 self)
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The class of mutually unbiased Hadamard (MUH) matrices is studied. We show that the number of MUH matrices of order 4n 2, n odd is at most 2 and that the bound is attained for n = 1,3. Furthermore, we find a lower bound for the number of MUH matrices of order 16n 2, assuming the existence of a Hadamard matrix of order 4n. An extension to unbiased weighing matrices is also presented.
Recovering Signals from Lowpass Data
 IEEE Trans. Signal Process
, 2010
"... Abstract—The problem of recovering a signal from its low frequency components occurs often in practical applications due to the lowpass behavior of many physical systems. Here, we study in detail conditions under which a signal can be determined from its lowfrequency content. We focus on signals in ..."
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Cited by 3 (3 self)
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Abstract—The problem of recovering a signal from its low frequency components occurs often in practical applications due to the lowpass behavior of many physical systems. Here, we study in detail conditions under which a signal can be determined from its lowfrequency content. We focus on signals in shiftinvariant spaces generated by multiple generators. For these signals, we derive necessary conditions on the cutoff frequency of the lowpass filter as well as necessary and sufficient conditions on the generators such that signal recovery is possible. When the lowpass content is not sufficient to determine the signal, we propose appropriate preprocessing that can improve the reconstruction ability. In particular, we show that modulating the signal with one or more mixing functions prior to lowpass filtering, can ensure the recovery of the signal in many cases, and reduces the necessary bandwidth of the filter. Index Terms—Lowpass signals, sampling, shiftinvariant spaces. I.