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Conjugacy Classes and Class Number
Integers, 2009AbstractIt is shown that the conjugacy classes of integral matrices with a given irreducible characteristic polynomial is in bijection with the class group of a corresponding order in an algebraic number field.
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On the Number of Classes of Binary Matrices
IEEE Transactions on Computers, 1973Cellular switching theory gives rise to the problems of counting the number of equivalence classes of m X n matrices of zeros and ones under: 1) row and column permutations; and 2) row and column permutations together with column complementations. A number of techniques are given for the solution of these problems.
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Philosophy of Science, 1941
To bring clearly before the mind what is meant by class and to distinguish this notion from all the notions to which it is allied, is one of the most difficult and important problems of mathematical philosophy.”When Russell wrote this in 1903, he could illustrate the difficulty of the problem by his own confusing attempt at a solution.
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To bring clearly before the mind what is meant by class and to distinguish this notion from all the notions to which it is allied, is one of the most difficult and important problems of mathematical philosophy.”When Russell wrote this in 1903, he could illustrate the difficulty of the problem by his own confusing attempt at a solution.
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Estimation of the Number of Classes in a Population
Biometrical Journal, 1988AbstractThe problem of estimating M, the number of classes in a population, is formulated as an occupancy problem in which N items are drawn from M urns. Under the assumption of a uniform distribution for the number of classes in the population, the sufficient statistic for M, which is the number of distinct classes observed, does not depend upon the ...
Arnold, Barry C., Beaver, Robert J.
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On the Class Numbers of Algebraic Number Fields
Journal of Mathematical Sciences, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A "Popular" Class Number Formula
The American Mathematical Monthly, 1994we get x1 + X3 + * * * +X45 = 76 and X2 + X4 + * * * +X46 = 131, whose difference is 55. Hence the average of x1, X3, . . . iS 323, whereas the average Of X27 X4, . . . iS c 16 J23 The Theorem holds for the digit expansion of 1/p with respect to an arbitrary basis g E @, g > 2, provided that g is a primitive root mod p.
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Invertibility and Class Number of Orders
Canadian Journal of Mathematics, 1971This paper continues the work begun in [ 5 ] and concerns the invertibility of modules in a finite-dimensional, symmetric algebra L with 1 over a field.
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ON THE CLASS-RECONSTRUCTION NUMBER OF TREES
The Quarterly Journal of Mathematics, 1988It is shown that for each tree T one can always find three vertex-deleted subgraphs in the deck of T which uniquely determine T in the class of trees, i.e., these graphs do not all appear in the deck of any other (nonisomorphic) tree.
Harary, Frank, Lauri, Josef
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2002
Abstract The conceptual clarification described in the previous chapter dispenses with infinitesimals. But that was not felt to be good enough: some account of the real numbers was also needed. This chapter first explains that need and presents the two best known accounts of real numbers.
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Abstract The conceptual clarification described in the previous chapter dispenses with infinitesimals. But that was not felt to be good enough: some account of the real numbers was also needed. This chapter first explains that need and presents the two best known accounts of real numbers.
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