Last Updated：2025/12/02

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(mathematics) Pertaining to a permutation such that there is at most one left and one right descent (at most one index i and one index j, such that wsᵢ < w and sⱼw < w).

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bigrassmannian

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Source Word

bigrassmannian

Adjective

not-comparable

(mathematics) Pertaining to a permutation such that there is at most one left and one right descent (at most one index i and one index j, such that wsᵢ < w and sⱼw < w).

Japanese Meaning

数学において、ある順列について、左側から見た場合に最大で1か所、右側から見た場合にも最大で1か所のみ“降下”（すなわち、順列の位置iまたはjにおいて、左右の隣接要素との比較で降下が認められる状態）が存在するという性質に関連する用語です。

What is this buttons?

We studied a bigrassmannian permutation that illustrated the structure of its left and right descents.

Google Translation / DeepL Translation

私たちは、左側の降下が高々1つ、右側の降下が高々1つである置換を研究し、それが降下の構造を示す例となった。

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Sense（1）

(mathematics) Pertaining to a permutation such that there is at most one left and one right descent (at most one index i and one index j, such that wsᵢ < w and sⱼw < w).

Combining this with the construction of Chern classes with coefficients in the bigrassmannian complexes, we get, for the weights up to four, local explicit formulas for the Chern classes in the rational Deligne cohomology via polylogarithms.

Google Translation / DeepL Translation

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bigrassmannian

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