Results 11 to 20 of about 116,873 (193)
Accessible and Deterministic Automata: Enumeration and Boltzmann Samplers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2006 We present a bijection between the set $\mathcal{A}_n$ of deterministic and accessible automata with $n$ states on a $k$-letters alphabet and some diagrams, which can themselves be represented as partitions of the set $[\![ 1..(kn+1) ]\!]$ into $n$ non ...
Frédérique Bassino, Cyril Nicaud
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Subwords and Plane Partitions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Using the powerful machinery available for reduced words of type $B$, we demonstrate a bijection between centrally symmetric $k$-triangulations of a $2(n + k)$-gon and plane partitions of height at most $k$ in a square of size $n$.
Zachary Hamaker, Nathan Williams
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Another bijection between $2$-triangulations and pairs of non-crossing Dyck paths [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 A $k$-triangulation of the $n$-gon is a maximal set of diagonals of the $n$-gon containing no subset of $k+1$ mutually crossing diagonals. The number of $k$-triangulations of the $n$-gon, determined by Jakob Jonsson, is equal to a $k \times k$ Hankel ...
Carlos M. Nicolás
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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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Crystal Interpretation of Kerov-Kirillov-Reshetikhin Bijection II. Proof for sl_n Case [PDF]
, 2007 In proving the Fermionic formulae, combinatorial bijection called the Kerov--Kirillov--Reshetikhin (KKR) bijection plays the central role. It is a bijection between the set of highest paths and the set of rigged configurations.
A. Kuniba +25 more
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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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Involve, a Journal of Mathematics, 2021 We investigate the dynamics of the well-known RSK bijection on permutations when iterated on various reading words of the recording tableau. In the setting of the ordinary (row) reading word, we show that there is exactly one fixed point per partition shape, and that it is always reached within two steps from any starting permutation.
Gillespie, Maria +3 more
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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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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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Limit Shapes via Bijections [PDF]
Combinatorics, Probability and Computing, 2018 We compute the limit shape for several classes of restricted integer partitions, where the restrictions are placed on the part sizes rather than the multiplicities. Our approach utilizes certain classes of bijections which map limit shapes continuously in the plane. We start with bijections outlined in [43], and extend them to include limit shapes with
DeSalvo, Stephen, Pak, Igor
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