Results 31 to 40 of about 115,299 (267)
Magic Square and Arrangement of Consecutive Integers That Avoids k-Term Arithmetic Progressions
Mathematics, 2021 In 1977, Davis et al. proposed a method to generate an arrangement of [n]={1,2,…,n} that avoids three-term monotone arithmetic progressions. Consequently, this arrangement avoids k-term monotone arithmetic progressions in [n] for k≥3.
Kai An Sim, Kok Bin Wong
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New Hopf Structures on Binary Trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 The multiplihedra $\mathcal{M}_{\bullet} = (\mathcal{M}_n)_{n \geq 1}$ form a family of polytopes originating in the study of higher categories and homotopy theory. While the multiplihedra may be unfamiliar to the algebraic combinatorics community, it is
Stefan Forcey +2 more
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J. Integer Seq., 2015 Define a sequence of positive integers by the rule that a(n) = n for 1 <= n <= 3, and for n >= 4, a(n) is the smallest number not already in the sequence which has a common factor with a(n-2) and is relatively prime to a(n-1). We show that this is a permutation of the positive integers. The remarkable graph of this sequence consists of runs of
David L. Applegate +5 more
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Interlocked Permutations [PDF]
SIAM Journal on Discrete Mathematics, 2019 The zero-error capacity of channels with a countably infinite input alphabet formally generalises Shannon's classical problem about the capacity of discrete memoryless channels. We solve the problem for three particular channels. Our results are purely combinatorial and in line with previous work of the third author about permutation capacity.
Cohen, Gérard +2 more
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Enumeration of the distinct shuffles of permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 A shuffle of two words is a word obtained by concatenating the two original words in either order and then sliding any letters from the second word back past letters of the first word, in such a way that the letters of each original word remain spelled ...
Camillia Smith Barnes
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Partitioned Cacti: a Bijective Approach to the Cycle Factorization Problem [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 In this paper we construct a bijection for partitioned 3-cacti that gives raise to a new formula for enumeration of factorizations of the long cycle into three permutations with given number of cycles.
Gilles Schaeffer, Ekaterina Vassilieva
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Homogeneous Permutations [PDF]
The Electronic Journal of Combinatorics, 2002 There are just five Fraïssé classes of permutations (apart from the trivial class of permutations of a singleton set); these are the identity permutations, reversing permutations, composites (in either order) of these two classes, and all permutations. The paper also discusses infinite generalisations of permutations, and the connection with Fraïssé's ...
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Permutations by Interchanges [PDF]
The Computer Journal, 1963 Methods for obtaining all possible permutations of a number of objects, in which each permutation differs from its predecessor only by the interchange of two of the objects, are discussed. Details of two programs which produce these permutations are given, one allowing a specified position to be filled by each of the objects in a predetermined order ...
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Determinant of binary circulant matrices
Special Matrices, 2019 This article gives a closed-form expression for the determinant of binary circulant matrices.
Hariprasad M.
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Profiles of Permutations [PDF]
The Electronic Journal of Combinatorics, 2009 This paper develops an analogy between the cycle structure of, on the one hand, random permutations with cycle lengths restricted to lie in an infinite set $S$ with asymptotic density $\sigma$ and, on the other hand, permutations selected according to the Ewens distribution with parameter $\sigma$.
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