Results 31 to 40 of about 117,839 (222)

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

Some asymptotic bijections

Journal of Combinatorial Theory, Series A, 1985
Let \(S_ n\supseteq S_ n'\), \(T_ n\supseteq T_ n'\) with \(| S_ n| \sim | S_ n'|\) and \(| T_ n\sim | T_ n'|\) as \(n\to \infty\). If there exist bijections \(\Phi_ n\) from \(S_ n'\) to \(T_ n'\) then \(\Phi_ n\) is called an asymptotic bijection from \(S_ n\) to \(T_ n\). Using this idea, the authors verify the partition formula: \(B_ r=e^{-1}\sum^{\
Edward A. Bender, Doron Zeilberger
openaire   +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

Bijections for Entringer families

European Journal of Combinatorics, 2011
André proved that the number of alternating permutations on $\{1, 2, \dots, n\}$ is equal to the Euler number $E_n$. A refinement of André's result was given by Entringer, who proved that counting alternating permutations according to the first element gives rise to Seidel's triangle $(E_{n,k})$ for computing the Euler numbers.
Gelineau, Yoann, Shin, Heesung, Zeng, Jiang   +2 more
openaire   +4 more sources

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

Symmetric functions: a bijective identity [PDF]

Proceedings of the American Mathematical Society, 1988
We give a bijective proof of a classical identity which we have named the cyclotomic identity.
Metropolis, N., Rota, Gian-Carlo
openaire   +2 more sources

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

An explicit bijection between semistandard tableaux and non-elliptic sl_3 webs [PDF]

, 2012
The sl_3 spider is a diagrammatic category used to study the representation theory of the quantum group U_q(sl_3). The morphisms in this category are generated by a basis of non-elliptic webs.
Russell, Heather M.
core   +3 more sources