Dual filtered graphs

Rebecca Patrias, Pavlo Pylyavskyy

Research output: Contribution to journalConference articlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1-12
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - 2015
Event27th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2015 - Daejeon, Korea, Republic of
Duration: Jul 6 2015Jul 10 2015

Bibliographical note

Funding Information:
†Email: patri080@umn.edu. R.P. was supported by NSF grant DMS-1148634. ‡Email: ppylyavs@umn.edu. P.P. was supported by NSF grants DMS-1068169, DMS-1148634, DMS-1351590, and Sloan Fellowship.

Publisher Copyright:
© 2015 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France

Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

Keywords

  • Bialgebras
  • Dual graded graphs
  • K-theory

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