On the distribution of depths in increasing trees.
Kuba, Markus, Wagner, Stephan (2010)
The Electronic Journal of Combinatorics [electronic only]
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Kuba, Markus, Wagner, Stephan (2010)
The Electronic Journal of Combinatorics [electronic only]
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Novelli, Jean-Christophe, Thibon, Jean-Yves (2009)
The Electronic Journal of Combinatorics [electronic only]
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Leroux, Philippe (2007)
Journal of Integer Sequences [electronic only]
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Leroux, Philippe (2006)
International Journal of Mathematics and Mathematical Sciences
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Singer, Dan (2001)
The Electronic Journal of Combinatorics [electronic only]
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Manes, K., Sapounakis, A., Tasoulas, I., Tsikouras, P. (2009)
Journal of Integer Sequences [electronic only]
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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.
Chaudhuri, R., Höft, H. (1991)
International Journal of Mathematics and Mathematical Sciences
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Singer, Dan W. (1998)
The Electronic Journal of Combinatorics [electronic only]
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Joachim Kock (2013)
Open Mathematics
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We exhibit a monoidal structure on the category of finite sets indexed by P-trees for a finitary polynomial endofunctor P. This structure categorifies the monoid scheme (over Spec ℕ) whose semiring of functions is (a P-version of) the Connes-Kreimer bialgebra H of rooted trees (a Hopf algebra after base change to ℤ and collapsing H 0). The monoidal structure is itself given by a polynomial functor, represented by three easily described set maps; we show that these maps are the same as...
Ana Pasztor (1983)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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F.A. Muntaner-Batle, Miquel Rius-Font (2008)
Discussiones Mathematicae Graph Theory
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We study the structure of path-like trees. In order to do this, we introduce a set of trees that we call expandable trees. In this paper we also generalize the concept of path-like trees and we call such generalization generalized path-like trees. As in the case of path-like trees, generalized path-like trees, have very nice labeling properties.