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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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Infinite Classes of Covering Numbers
Canadian Mathematical Bulletin, 2000AbstractLet D be a family of k-subsets (called blocks) of a v-set X(v). Then D is a (v, k, t) covering design or covering if every t-subset of X(v) is contained in at least one block of D. The number of blocks is the size of the covering, and the minimum size of the covering is called the covering number.
Bluskov, I., Greig, M., Heinrich, K.
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Class numbers of group extensions
Journal of Group Theory, 2010Let \(X\) be a finite group and \(N\) a normal subgroup of \(X\). Let \(G=X/N\). A well-known formula due to Gallagher states that \(k(X)=\sum_{\theta\in\text{Irr}(N)}k_\theta(I_G(\theta))/|G:I_G(\theta)|\). Here \(k(X)\) denotes the number of conjugacy classes of \(X\), \(\text{Irr}(N)\) is the set of irreducible complex characters of \(N\), \(I_G ...
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On virtual classes and real numbers
Journal of Symbolic Logic, 1950In a simple, applied functional calculus of first order (i.e., one admitting no functional variables but at least one functional constant), abstracts or schematic expressions may be introduced to play the role of variables over designatable sets or classes.
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On Dirichlet's Class Number Formula
Journal of the London Mathematical Society, 1978This paper gives a new arithmetic proof of Dirichlet's formula for the number of distinct classes of integral primitive binary quadratic forms of a given negative discriminant. Comparing his proof with the arithmetic proof of \textit{B. A. Venkov} [Math. Z. 33, 350--374 (1931; Zbl 0001.12003; JFM 57.0194.02)], the author underlines: ``The main interest
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