Results 31 to 40 of about 8,688 (230)

A further correspondence between $(bc,\bar{b})$-parking functions and $(bc,\bar{b})$-forests [PDF]

Discrete Mathematics & Theoretical Computer Science, 2009
For a fixed sequence of $n$ positive integers $(a,\bar{b}) := (a, b, b,\ldots, b)$, an $(a,\bar{b})$-parking function of length $n$ is a sequence $(p_1, p_2, \ldots, p_n)$ of positive integers whose nondecreasing rearrangement $q_1 \leq q_2 \leq \cdots ...
Heesung Shin, Jiang Zeng
doaj   +1 more source

Arc-Coloured Permutations [PDF]

Discrete Mathematics & Theoretical Computer Science, 2013
The equidistribution of many crossing and nesting statistics exists in several combinatorial objects like matchings, set partitions, permutations, and embedded labelled graphs.
Lily Yen
doaj   +1 more source

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
doaj   +1 more source

A Bijection for Tricellular Maps

ISRN Discrete Mathematics, 2013
We give a bijective proof for a relation between unicellular, bicellular, and tricellular maps. These maps represent cell complexes of orientable surfaces having one, two, or three boundary components. The relation can formally be obtained using matrix theory (Dyson, 1949) employing the Schwinger-Dyson equation (Schwinger, 1951).
Han, Hillary Siwei, Reidys, Christian
openaire   +4 more sources

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

A Pipe Dream Perspective on Totally Symmetric Self-Complementary Plane Partitions

Forum of Mathematics, Sigma
We characterize totally symmetric self-complementary plane partitions (TSSCPP) as bounded compatible sequences satisfying a Yamanouchi-like condition. As such, they are in bijection with certain pipe dreams.
Daoji Huang, Jessica Striker
doaj   +1 more source

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 bijection for partitions simultaneously $s$-regular and $t$-distinct

, 2022
In this note a bijection is constructed between the set of partitions of n simultaneously s-regular and t-distinct, and those simultaneously t-regular and s-distinct. Some implications of the map are discussed.
Keith, William J.
core  

A bijection between permutations and a subclass of TSSCPPs [PDF]

Discrete Mathematics & Theoretical Computer Science, 2013
We define a subclass of totally symmetric self-complementary plane partitions (TSSCPPs) which we show is in direct bijection with permutation matrices. This bijection maps the inversion number of the permutation, the position of the 1 in the last column,
Jessica Striker
doaj   +1 more source

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
doaj   +1 more source