Results 21 to 30 of about 246,865 (191)
On additive partitions of integers
Discrete Mathematics, 1978 Let \(U=\{u_n\}\), \(u_{n+2}=u_{n+1}+u_n\), \(n\geq 1\), \(u_1=1\), \(u_2> u_1\), be a linear recurrence sequence. It is shown that the set of positive integers can be partitioned uniquely into two disjoint subsets such that the sum of any two distinct numbers from any one set can never be in \(U\).
Krishnaswami Alladi +2 more
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A PROOF OF ANDREWS’ CONJECTURE ON PARTITIONS WITH NO SHORT SEQUENCES
Forum of Mathematics, Sigma, 2019 Our main result establishes Andrews’ conjecture for the asymptotic of the generating function for the number of integer partitions of $n$ without $k$ consecutive parts.
DANIEL M. KANE, ROBERT C. RHOADES
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European Journal of Combinatorics, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Konrad Engel +2 more
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A phase transition in the distribution of the length of integer partitions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We assign a uniform probability to the set consisting of partitions of a positive integer $n$ such that the multiplicity of each summand is less than a given number $d$ and we study the limiting distribution of the number of summands in a random ...
Dimbinaina Ralaivaosaona
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Geometric polynomials and integer partitions [PDF]
, 2021 In this paper, we show that the geometric polynomials can be expressed as sums over integer partitions in two different ways. New formulas involving geometric numbers, Bernoulli numbers, and Genocchi numbers are derived in this ...
Merca, Mircea
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An Efficient Algorithm to Test Forcibly-connectedness of Graphical Degree Sequences
Theory and Applications of Graphs, 2018 We present an algorithm to test whether a given graphical degree sequence is forcibly connected or not and prove its correctness. We also outline the extensions of the algorithm to test whether a given graphical degree sequence is forcibly $k$-connected ...
Kai Wang
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The Fractal and The Recurrence Equations Concerning The Integer Partitions [PDF]
, 2022 This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the pentagonal number
Zhang, Meng
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Communal Partitions of Integers
Integers, 2012 Abstract.There is a well-known formula due to Andrews that counts the number of incongruent triangles with integer sides and a fixed perimeter.
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Composite Fermions and Integer Partitions
Journal of Combinatorial Theory, Series A, 2001 The authors prove the unimodality of integer partitions with at most \(a\) parts, all parts less than or equal to \(b\), that are required to contain either repeated or consecutive parts. The proof uses the KOH theorem [\textit{D. Zeilberger}, Am. Math. Mon. 96, No. 7, 590-602 (1989; Zbl 0726.05005)].
Arthur T. Benjamin +3 more
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Cutting plane methods for general integer programming [PDF]
, 1993 Integer programming (IP) problems are difficult to solve due to the integer restrictions imposed on them. A technique for solving these problems is the cutting plane method.
Mitra, G +5 more
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