DHD-puzzles

Sabine Beil

doi:10.46298/dmtcs.6332

Abstract

In this work triangular puzzles that are composed of unit triangles with labelled edges are considered. To be more precise, the labelled unit triangles that we allow are on the one hand the puzzle pieces that compute Schubert calculus and on the other hand the flipped K-theory puzzle piece. The motivation for studying such puzzles comes from the fact that they correspond to a class of oriented triangular fully packed loop configurations. The main result that is presented is an expression for the number of these puzzles with a fixed boundary in terms of Littlewood- Richardson coefficients.

Highlights

In [5], triangular puzzles were introduced to compute Schubert calculus. These triangular puzzles together with additional puzzle pieces that were established in [3] will be the central objects in this article
Their study is motivated by their correspondence to a class of oriented triangular fully packed loop configurations as they were defined in [3]
The puzzle pieces that were introduced in [5] are the following unit triangles with labelled edges: In the following, they will be referred to as ordinary puzzle pieces

Summary

Sabine Beil

28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés

Introduction

The map Q

BR B