Noncommutative Catalan numbers

Berenstein, Arkady; Retakh, Vladimir

doi:10.1007/s00026-019-00473-4

アイテム詳細

登録内容を編集ファイル形式で保存

一時保存へ追加

タグ情報を表示リリース履歴を表示詳細要約

公開

学術論文

Noncommutative Catalan numbers

MPS-Authors

/persons/resource/persons234949

Berenstein, Arkady
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1007/s00026-019-00473-4
(出版社版)

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

フルテキスト (公開)

arXiv:1708.03316.pdf
(プレプリント), 251KB

付随資料 (公開)

There is no public supplementary material available

引用

Berenstein, A., & Retakh, V. (2019). Noncommutative Catalan numbers. Annals of Combinatorics, 23(3-4), 527-547. doi:10.1007/s00026-019-00473-4.

引用: https://hdl.handle.net/21.11116/0000-0006-3EFD-9

要旨

The goal of this paper is to introduce and study noncommutative Catalan
numbers $C_n$ which belong to the free Laurent polynomial algebra in $n$
generators. Our noncommutative numbers admit interesting (commutative and
noncommutative) specializations, one of them related to Garsia-Haiman
$(q,t)$-versions, another -- to solving noncommutative quadratic equations. We
also establish total positivity of the corresponding (noncommutative) Hankel
matrices $H_m$ and introduce accompanying noncommutative binomial coefficients.