Results 31 to 40 of about 3,063 (228)
Extending from bijections between marked occurrences of patterns to all occurrences of patterns [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We consider two recent open problems stating that certain statistics on various sets of combinatorial objects are equidistributed. The first, posed by Anders Claesson and Svante Linusson, relates nestings in matchings on $\{1,2,\ldots,2n\}$ to ...
Jeffrey Remmel, Mark Tiefenbruck
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A new combinatorial identity for unicellular maps, via a direct bijective approach. [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We give a bijective operation that relates unicellular maps of given genus to unicellular maps of lower genus, with distinguished vertices. This gives a new combinatorial identity relating the number $\epsilon_g(n)$ of unicellular maps of size $n$ and ...
Guillaume Chapuy
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The Bijectivity of the Antipode Revisited [PDF]
Communications in Algebra, 2011 We provide a very short approach to several fundamental results for Hopf algebras with nonzero integrals. Besides being short, our approach is the first to prove the bijectivity of the antipode without using the uniqueness of the integrals of Hopf algebras and to obtain the uniqueness of integrals as a corollary in a way similar to the classical theory
Şerban Raianu, Miodrag Cristian Iovanov
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A bijection between planar constellations and some colored Lagrangian trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2003 Constellations are colored planar maps that generalize different families of maps (planar maps, bipartite planar maps, bi-Eulerian planar maps, planar cacti, ...) and are strongly related to factorizations of permutations.
Cedric Chauve
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The Ellis semigroup of bijective substitutions [PDF]
Groups, Geometry, and Dynamics, 2021 For topological dynamical systems (X,T,\sigma) with abelian group T , which admit an equicontinuous factor \pi:(X,T,\sigma)\to (Y,T,\delta) , the Ellis semigroup
Johannes Kellendonk, Reem Yassawi
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Modified Growth Diagrams, Permutation Pivots, and the BWX Map $\phi^*$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 In their paper on Wilf-equivalence for singleton classes, Backelin, West, and Xin introduced a transformation $\phi^*$, defined by an iterative process and operating on (all) full rook placements on Ferrers boards. Bousquet-Mélou and Steingrimsson proved
Jonathan Bloom, Dan Saracino
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On the SEL Egyptian fraction expansion for real numbers
AIMS Mathematics, 2022 In the authors' earlier work, the SEL Egyptian fraction expansion for any real number was constructed and characterizations of rational numbers by using such expansion were established.
Mayurachat Janthawee +1 more
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International Electronic Journal of Algebra, 2016 Given a finite acyclic quiver Q with path algebra kQ, Ingalls and Thomas have exhibited a bijection between the set of Morita equivalence classes of support-tilting modules and the set of thick subcategories of mod kQ and they have collected a large number of further bijections with these sets.
Obaid, M. A. A. +3 more
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Journal of Combinatorial Theory, Series A, 1985 Let \(S_ n\supseteq S_ n'\), \(T_ n\supseteq T_ n'\) with \(| S_ n| \sim | S_ n'|\) and \(| T_ n\sim | T_ n'|\) as \(n\to \infty\). If there exist bijections \(\Phi_ n\) from \(S_ n'\) to \(T_ n'\) then \(\Phi_ n\) is called an asymptotic bijection from \(S_ n\) to \(T_ n\). Using this idea, the authors verify the partition formula: \(B_ r=e^{-1}\sum^{\
Doron Zeilberger, Edward A. Bender
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Classification of bijections between 321- and 132-avoiding permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 It is well-known, and was first established by Knuth in 1969, that the number of 321-avoiding permutations is equal to that of 132-avoiding permutations. In the literature one can find many subsequent bijective proofs confirming this fact.
Anders Claesson, Sergey Kitaev
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