Results 71 to 80 of about 208 (162)

and [PDF]

, 2009
. We study the descent distribution over the set of centrosymmetric permutations that avoid a pattern of length 3. In the most puzzling case, namely, τ = 123 and n even, our main tool is a bijection that associates a Dyck pre x of length 2n to every ...
Marilena Barnabei, Matteo Silimbani, Flavio Bonetti   +2 more
core  

Symmetric edge polytopes and matching generating polynomials [PDF]

, 2021
Symmetric edge polytopes \(\mathcal{A}_G\) of type A are lattice polytopes arising from the root system \(A_n\) and finite simple graphs \(G\). There is a connection between \(\mathcal{A}_G\) and the Kuramoto synchronization model in physics.
Ohsugi, Hidefumi, Tsuchiya, Akiyoshi
core   +1 more source

Parity Reversing Involutions on Plane Trees and 2-Motzkin Paths

, 2005
. The problem of counting plane trees with n edges and an even or an odd number of leaves was studied by Eu, Liu and Yeh, in connection with an identity on coloring nets due to Stanley.
Chen, William Y.C., Shapiro, Louis W., Louis W. Shapiro, Laura L. M. Yang, William Y. C. Chen, Yang, Laura L.M.   +5 more
core   +1 more source

The permutation class Av(4213,2143) [PDF]

Discrete Mathematics & Theoretical Computer Science, 2017
We determine the structure of permutations avoiding the patterns 4213 and 2143. Each such permutation consists of the skew sum of a sequence of plane trees, together with an increasing sequence of points above and an increasing sequence of points to its ...
David Bevan
doaj   +1 more source

Intervals in the greedy Tamari posets [PDF]

, 2023
We consider a greedy version of the \(m\)-Tamari order defined on \(m\)-Dyck paths, recently introduced by Dermenjian. Inspired by intriguing connections between intervals in the ordinary {1-}Tamari order and planar triangulations, and more generally by ...
Chapoton, Frédéric, Bousquet-Mélou, Mireille   +1 more
core   +1 more source

Proofs of Conjectures about Pattern-Avoiding Linear Extensions [PDF]

Discrete Mathematics & Theoretical Computer Science, 2019
After fixing a canonical ordering (or labeling) of the elements of a finite poset, one can associate each linear extension of the poset with a permutation.
Colin Defant
doaj   +1 more source

On nested block designs geometry

Orthogonal designs, Orthogonal block structure, General balance, Commutativity of projectors, Commutative quadratic subspace, Primary 62J05, Secondary 05A15, 15A18,
Radosław Kala
core   +1 more source

A refined enumeration of hex trees and related polynomials

, 2015
A hex tree is an ordered tree of which each vertex has updegree 0, 1, or 2, and an edge from a vertex of updegree 1 is either left, median, or right. We present a refined enumeration of symmetric hex trees via a generalized binomial transform.
Richard P. Stanleyb, Stanley, Richard P, Hana Kim, Kim, Hana, Hana Kima, Richard P. Stanley   +5 more
core   +1 more source

Growing and Destroying Catalan-Stanley Trees [PDF]

Discrete Mathematics & Theoretical Computer Science, 2018
Stanley lists the class of Dyck paths where all returns to the axis are of odd length as one of the many objects enumerated by (shifted) Catalan numbers.
Benjamin Hackl, Helmut Prodinger
doaj   +1 more source

Distribution of sets of descent tops and descent bottoms on restricted permutations [PDF]

Discrete Mathematics & Theoretical Computer Science
In this note, we prove some and conjecture other results regarding the distribution of descent top and descent bottom sets on some pattern-avoiding permutations.
Alexander Burstein
doaj   +1 more source