Rebecca Patrias ; Pavlo Pylyavskyy - Dual filtered graphs

dmtcs:2515 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) - https://doi.org/10.46298/dmtcs.2515
Dual filtered graphsArticle

Authors: Rebecca Patrias 1; Pavlo Pylyavskyy ORCID1

  • 1 School of Mathematics

We define a $K$ -theoretic analogue of Fomin’s dual graded graphs, which we call dual filtered graphs. The key formula in the definition is $DU - UD = D + I$. Our major examples are $K$ -theoretic analogues of Young’s lattice, the binary tree, and the graph determined by the Poirier-Reutenauer Hopf algebra. Most of our examples arise via two constructions, which we call the Pieri construction and the Möbius construction. The Pieri construction is closely related to the construction of dual graded graphs from a graded Hopf algebra, as described in Bergeron-Lam-Li, Nzeutchap, and Lam-Shimozono. The Möbius construction is more mysterious but also potentially more important, as it corresponds to natural insertion algorithms.


Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Imported on: November 21, 2016
Keywords: dual graded graphs,$K$ -theory,bialgebras,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • RTG in Combinatorics; Funder: National Science Foundation; Code: 1148634
  • Some questions in total positivity and cluster algebras; Funder: National Science Foundation; Code: 1068169
  • CAREER: Algebraic Combinatorics and URE; Funder: National Science Foundation; Code: 1351590

2 Documents citing this article

Consultation statistics

This page has been seen 263 times.
This article's PDF has been downloaded 311 times.