Inversion of integral series enumerating planar trees.
Loday, Jean-Louis (2005)
Séminaire Lotharingien de Combinatoire [electronic only]
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Displaying similar documents to “Free dendriform algebras. I: A parenthesis setting.”
Inversion of integral series enumerating planar trees.
A simple symmetry generating operads related to rooted planar -ary trees and polygonal numbers.
Leroux, Philippe (2007)
Journal of Integer Sequences [electronic only]
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Sets with two associative operations
Teimuraz Pirashvili (2003)
Open Mathematics
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In this paper we consider duplexes, which are sets with two associative binary operations. Dimonoids in the sense of Loday are examples of duplexes. The set of all permutations carries a structure of a duplex. Our main result asserts that it is a free duplex with an explicitly described set of generators. The proof uses a construction of the free duplex with one generator by planary trees.
Right-cancellability of a family of operations on binary trees.
Duchon, Philippe (1998)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Hook length formulas for trees by Han's expansion.
Chen, William Y.C., Gao, Oliver X.Q., Guo, Peter L. (2009)
The Electronic Journal of Combinatorics [electronic only]
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Probabilistic proofs of hook length formulas involving trees.
Sagan, Bruce E. (2009)
Séminaire Lotharingien de Combinatoire [electronic only]
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The height of -binary search trees.
Drmota, Michael, Prodinger, Helmut (2002)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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A semantic construction of two-ary integers
Gabriele Ricci (2005)
Discussiones Mathematicae - General Algebra and Applications
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To binary trees, two-ary integers are what usual integers are to natural numbers, seen as unary trees. We can represent two-ary integers as binary trees too, yet with leaves labelled by binary words and with a structural restriction. In a sense, they are simpler than the binary trees, they relativize. Hence, contrary to the extensions known from Arithmetic and Algebra, this integer extension does not make the starting objects more complex. We use a semantic construction to get this extension....
Betweenness spaces and tree algebras
Jánis Círulis (1986)
Časopis pro pěstování matematiky
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On Catalan trees and the Jacobian conjecture.
Singer, Dan (2001)
The Electronic Journal of Combinatorics [electronic only]
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Analysis of some statistics for increasing tree families.
Panholzer, Alois, Prodinger, Helmut (2004)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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