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 language||English (US)|
|Number of pages||12|
|Journal||Discrete Mathematics and Theoretical Computer Science|
|State||Published - Jan 1 2015|
|Event||27th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2015 - Daejeon, Korea, Republic of|
Duration: Jul 6 2015 → Jul 10 2015
- Dual graded graphs