Triangular fully packed loop configurations of excess 2
type: Item
instance of: scholarly article
title: Triangular fully packed loop configurations of excess 2
zbMATH Open document ID: 1351.05016
author: Sabine Beil
published in: The Electronic Journal of Combinatorics
publication date: 2016-12-06T00:00:00Z
full work available at URL: v23i4p14
review text: Summary: Triangular fully packed loop configurations (TFPLs) came up in the study of fully packed loop configurations on a square (FPLs) corresponding to link patterns with a large number of nested arches. To a TFPL is assigned a triple \((u,v;w)\) of \(01\)-words encoding its boundary conditions which must necessarily satisfy that \(d(u)+d(v)\leq d(w)\), where \(d(u)\) denotes the number of inversions in \(u\). Wieland gyration, on the other hand, was invented to show the rotational invariance of the numbers of FPLs having given link patterns. Later, Wieland drift -- a map on TFPLs that is based on Wieland gyration -- was defined. The main contribution of this article will be a linear expression for the number of TFPLs with boundary \((u,v;w)\) where \(d(w)-d(u)-d(v)=2\) in terms of numbers of stable TFPLs, that is, TFPLs invariant under Wieland drift. This linear expression generalises already existing enumeration results for TFPLs with boundary \((u,v;w)\) where \(d(w)-d(u)-d(v)=0,1\).
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 6661366
zbMATH Keywords: triangular fully packed loop configurations
zbMATH Keywords: Wieland gyration
describes a project that uses: ROBBINS
MaRDI profile type: Publication
cites work: Triangular fully packed loop configurations of excess 2
cites work: Wieland drift for triangular fully packed loop configurations
cites work: Proof of the Razumov-Stroganov conjecture
cites work: On the number of fully packed loop configurations with a fixed associated matching
cites work: Fully packed loops in a triangle: matchings, paths and puzzles
cites work: Q4880965
cites work: Fully packed loop configurations in a triangle
cites work: Fully packed loop configurations in a triangle and Littlewood-Richardson coefficients
cites work: Refined counting of fully packed loop configurations
cites work: A large dihedral symmetry of the set of alternating sign matrices
cites work: Proof of the alternating sign matrix conjecture
cites work: On the counting of fully packed loop configurations: some new conjectures
description: scientific article; zbMATH DE number 6661366