Counting perfect matchings in polyominoes with an application to the dimer problem
P. John, H. Sachs, H. Zernitz (1987)
Applicationes Mathematicae
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P. John, H. Sachs, H. Zernitz (1987)
Applicationes Mathematicae
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M. N. Mukherjee, S. Raychaudhuri (1993)
Matematički Vesnik
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G. L. Garg, B. Kumar (1989)
Matematički Vesnik
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Tošić, Ratko, Vojvodić, Dušan (2000)
Novi Sad Journal of Mathematics
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Tomohiro Yamada (2005)
Colloquium Mathematicae
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We show that there is an effectively computable upper bound of odd perfect numbers whose Euler factors are powers of fixed exponent.
Min Tang, Xiao-Zhi Ren, Meng Li (2013)
Colloquium Mathematicae
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For a positive integer n, let σ(n) denote the sum of the positive divisors of n. Let d be a proper divisor of n. We call n a near-perfect number if σ(n) = 2n + d, and a deficient-perfect number if σ(n) = 2n - d. We show that there is no odd near-perfect number with three distinct prime divisors and determine all deficient-perfect numbers with at most two distinct prime factors.
Ivan Gutman (1991)
Publications de l'Institut Mathématique
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François Sigrist (2000)
Journal de théorie des nombres de Bordeaux
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Voronoï ’s algorithm is a method for obtaining the complete list of perfect -dimensional quadratic forms. Its generalization to -forms has the advantage of running in a lower-dimensional space, and furnishes a finite, and complete, classification of -perfect forms ( is a finite subgroup of . We study the standard, -dimensional irreducible representation of the cyclic group of order , and give the, often new, densest -forms. Perfect cyclotomic forms are completely classified...
R.A. Rankin (1964)
Mathematische Zeitschrift
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Giorgio Nordo (1997)
Commentationes Mathematicae Universitatis Carolinae
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In this paper we generalize the notion of of a Tychonoff space to a generic extension of any space by introducing the concept of . This allow us to simplify the treatment in a basic way and in a more general setting. Some [S], [S], and [D]’s results are improved and new characterizations for perfect (Hausdorff) extensions of spaces are obtained.
De Koninck, Jean-Marie, Ivić, Aleksandar (1998)
Publications de l'Institut Mathématique. Nouvelle Série
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