Hopf dreams

Nantel Bergeron; Cesar Ceballos; Vincent Pilaud

Hopf dreams

Nantel Bergeron
, Cesar Ceballos
, Vincent Pilaud

York University
C/o Faculty of Mathematics of the University of Vienna

Research output: Contribution to conference › Paper › peer-review

Abstract

We introduce a Hopf algebra structure on a family of reduced pipe dreams with a natural surjection onto a commutative Hopf algebra of permutations. We then study three Hopf subalgebras of permutations whose preimages by the surjection yield three relevant Hopf subalgebras of pipe dreams. The first is the Loday-Ronco Hopf algebra on binary trees, the second is related to a special family of lattice walks on the quarter plane, and the third is a Hopf algebra on n-trees related to n-Tamari lattices. The latter motivates a new notion of Hopf chains in the Tamari lattice with applications in the theory of multivariate diagonal harmonics.

Original language	English
Publication status	Published - 1 Jan 2019
Event	31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019 - Ljubljana, Slovenia Duration: 1 Jul 2019 → 5 Jul 2019

Conference

Conference	31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019
Country/Territory	Slovenia
City	Ljubljana
Period	1/07/19 → 5/07/19

Keywords

Hopf algebra
Multivariate diagonal harmonics
Pipe dream
Tamari lattice

Cite this

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title = "Hopf dreams",

abstract = "We introduce a Hopf algebra structure on a family of reduced pipe dreams with a natural surjection onto a commutative Hopf algebra of permutations. We then study three Hopf subalgebras of permutations whose preimages by the surjection yield three relevant Hopf subalgebras of pipe dreams. The first is the Loday-Ronco Hopf algebra on binary trees, the second is related to a special family of lattice walks on the quarter plane, and the third is a Hopf algebra on n-trees related to n-Tamari lattices. The latter motivates a new notion of Hopf chains in the Tamari lattice with applications in the theory of multivariate diagonal harmonics.",

keywords = "Hopf algebra, Multivariate diagonal harmonics, Pipe dream, Tamari lattice",

author = "Nantel Bergeron and Cesar Ceballos and Vincent Pilaud",

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TY - CONF

T1 - Hopf dreams

AU - Bergeron, Nantel

AU - Ceballos, Cesar

AU - Pilaud, Vincent

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We introduce a Hopf algebra structure on a family of reduced pipe dreams with a natural surjection onto a commutative Hopf algebra of permutations. We then study three Hopf subalgebras of permutations whose preimages by the surjection yield three relevant Hopf subalgebras of pipe dreams. The first is the Loday-Ronco Hopf algebra on binary trees, the second is related to a special family of lattice walks on the quarter plane, and the third is a Hopf algebra on n-trees related to n-Tamari lattices. The latter motivates a new notion of Hopf chains in the Tamari lattice with applications in the theory of multivariate diagonal harmonics.

AB - We introduce a Hopf algebra structure on a family of reduced pipe dreams with a natural surjection onto a commutative Hopf algebra of permutations. We then study three Hopf subalgebras of permutations whose preimages by the surjection yield three relevant Hopf subalgebras of pipe dreams. The first is the Loday-Ronco Hopf algebra on binary trees, the second is related to a special family of lattice walks on the quarter plane, and the third is a Hopf algebra on n-trees related to n-Tamari lattices. The latter motivates a new notion of Hopf chains in the Tamari lattice with applications in the theory of multivariate diagonal harmonics.

KW - Hopf algebra

KW - Multivariate diagonal harmonics

KW - Pipe dream

KW - Tamari lattice

M3 - Paper

AN - SCOPUS:85087888168

T2 - 31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019

Y2 - 1 July 2019 through 5 July 2019

ER -

Hopf dreams

Abstract

Conference

Keywords

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Cite this