Results 71 to 80 of about 158 (109)
GA2 index of some graph operations
, 2010 Let G = (V, E) be a graph. For e = uv ? E(G), nu (e) is the number of vertices of G lying closer to u than to v and nv (e) is the number of vertices of G lying closer to v than u. The GA2 index of G is defined as ?uv?E(G) 2?
G.H. Fath-Tabar +2 more
core +1 more source
Finite automata, probabilistic method, and occurrence enumeration of a pattern in words and permutations. [PDF]
SIAM J Discret Math, 2020 Mansour T, Rastegar R, Roitershtein A.
europepmc +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 +5 more
core +1 more source
, 2002 We derive the explicit formulas of the probability generating functions of the first hitting times of simple random walks on graphs with congestion points using group representations. 2000 Mathematics Subject Classification: 60G50, 60B15, 60K30, 05A15. 1.
Mihyun Kang
core
Slit-slide-sew bijections for oriented planar maps
We construct growth bijections for bipolar oriented planar maps and for Schnyder woods. These give direct combinatorial proofs of several counting identities for these objects. Our method mainly uses two ingredients.
Éric Fusy +2 more
core +1 more source
Piecewise-linear promotion and RSK in rectangles and moon polyominoes [PDF]
We study piecewise-linear and birational lifts of Schützenberger promotion, evacuation, and the RSK correspondence defined in terms of toggles. Using this perspective, we prove that certain chain statistics in rectangles shift predictably under the ...
Liu, Ricky Ini, Johnson, Joseph
core +1 more source
Boolean elements in the Bruhat order [PDF]
We show that a Weyl group element is boolean if and only if it avoids a set of Billey-Postnikov patterns, which we describe explicitly. Our proof is based on analysis of inversion sets, and it is in large part type-uniform.
Gao, Yibo, Hänni, Kaarel
core +1 more source
Repeatable patterns and the maximum multiplicity of a generator in a reduced word [PDF]
We study the maximum multiplicity \(\mathcal{M}(k,n)\) of a simple transposition \(s_k=(k \: k+1)\) in a reduced word for the longest permutation \(w_0=n \: n-1 \: \cdots \: 2 \: 1\), a problem closely related to much previous work on sorting networks ...
Gao, Yibo +4 more
core +1 more source
Blocks in cycles and k-commuting permutations. [PDF]
Springerplus, 2016 Moreno R, Rivera LM.
europepmc +1 more source
Permutation q-enumeration with the Schur row adder
, 2010 . We q-enumerate here, by the i-major index, the class of permutations of Sn with largest increasing subsequence of size n − k and increasing rst n − k entries. The result is obtained by a surprisingly straightforward use of the Schur row adder.
Adriano M. Garsia
core