Results 61 to 70 of about 132,418 (291)
Statistics on staircase tableaux, eulerian and mahonian statistics [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We give a simple bijection between some staircase tableaux and tables of inversion. Some nice properties of the bijection allows us to define some q-Eulerian polynomials related to the staircase tableaux.
Sylvie Corteel, Sandrine Dasse-Hartaut
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A combinatorial interpretation of the bijection of Goulden and Yong
AKCE International Journal of Graphs and Combinatorics, 2020 We define a dual of a graph, generalizing the definition of Goulden et al. (2002), which only applies to trees; then we reprove their main result using our new definition.
Kerry Ojakian
doaj +1 more source
A simple model of trees for unicellular maps [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We consider unicellular maps, or polygon gluings, of fixed genus. In FPSAC '09 the first author gave a recursive bijection transforming unicellular maps into trees, explaining the presence of Catalan numbers in counting formulas for these objects.
Guillaume Chapuy +2 more
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Dyck paths and pattern-avoiding matchings [PDF]
, 2007 How many matchings on the vertex set V={1,2,...,2n} avoid a given configuration of three edges? Chen, Deng and Du have shown that the number of matchings that avoid three nesting edges is equal to the number of matchings avoiding three pairwise crossing ...
Elizalde +3 more
core +2 more sources
A bijection between shrubs and series-parallel posets [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 Motivated by the theory of operads, we introduce new combinatorial objects, called shrubs, that generalize forests of rooted trees. We show that the species of shrubs is isomorphic to the species of series-parallel posets.
Frédéric Chapoton
doaj +1 more source
Linear Algebra and its Applications, 2006 AbstractIf A and B are square matrices such that AB=I, then BA=I automatically follows. We prove a combinatorial version of this result in the case where the entries of A and B count collections of signed, weighted objects. Specifically, we give an algorithm that transforms any given bijective proof of the identity AB=I into an explicit bijective proof
Anthony Mendes, Nicholas A. Loehr
openaire +2 more sources
Rigged configurations of type $D_4^{(3)}$ and the filling map [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We give a statistic preserving bijection from rigged configurations to a tensor product of Kirillov–Reshetikhin crystals $\otimes_{i=1}^{N}B^{1,s_i}$ in type $D_4^{(3)}$ by using virtualization into type $D_4^{(1)}$.
Travis Scrimshaw
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Journal of Combinatorial Theory, Series A, 1981 AbstractIn this paper we give a bijection between the partitions of n with parts congruent to 1 or 4 (mod 5) and the partitions of n with parts differing by at least 2. This bijection is obtained by a cut-and-paste procedure which starts with a partition in one class and ends with a partition in the other class.
Stephen C. Milne, Adriano M. Garsia
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Random discrete probability measures based on a negative binomial process
Canadian Journal of Statistics, EarlyView.Abstract A distinctive functional of the Poisson point process is the negative binomial process for which the increments are not independent but are independent conditional on an underlying gamma variable. Using a new point process representation for the negative binomial process, we generalize the Poisson–Kingman distribution and its corresponding ...
Sadegh Chegini, Mahmoud Zarepour
wiley +1 more source
Patterns in matchings and rook placements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Extending the notion of pattern avoidance in permutations, we study matchings and set partitions whose arc diagram representation avoids a given configuration of three arcs.
Jonathan Bloom, Sergi Elizalde
doaj +1 more source