Interval in a Coxeter group of type A6

asked 2022-02-16 12:33:03 +0200

BMC gravatar image

updated 2022-02-17 09:00:17 +0200

FrédéricC gravatar image

let [a,b] be a smooth interval in a Coxeter group of type A6 such that every ascent of a is an ascent of b. Is there a way of computing such interval in sage math?

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Welcome to Ask Sage! Thank you for your question.

slelievre gravatar imageslelievre ( 2022-02-16 14:01:28 +0200 )edit

Bruhat order ? weak order ? Shard-intersection order ? some other partial order ? And what does smooth mean ? And what do you mean by computing ? Are the elements a and b given ?

FrédéricC gravatar imageFrédéricC ( 2022-02-16 14:40:39 +0200 )edit

If you already have code for the setup, please provide it as a starting step for potential answerers.

slelievre gravatar imageslelievre ( 2022-02-16 14:59:17 +0200 )edit