Timeline for A property of monomials in a Schubert polynomial
Current License: CC BY-SA 3.0
6 events
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| Nov 13, 2014 at 18:36 | comment | added | darij grinberg | Oh -- so the Lehmer code bijection is a bijection between $\mathfrak{S}_{(\infty)} = \bigcup\limits_{n \geq 0}\mathfrak{S}_n$ and the set of weak compositions. I was never aware of this; it is a very nice fact! (Nicer than the well-known finite versions.) | |
| Nov 13, 2014 at 11:21 | comment | added | Allen Knutson | I don't understand the "stretched out". They are exactly the same as the usual ones, just reindexed, using the Lehmer code bijection. | |
| Nov 12, 2014 at 4:04 | comment | added | darij grinberg | Oh -- you are saying that Lascoux's Schubert polynomials are essentially the usual permutation-indexed Schubert polynomials, whose variables have been stretched out? | |
| Nov 12, 2014 at 2:39 | comment | added | Allen Knutson | Did you read about the Lehmer code? It gives a bijection between finite permutations of $\mathbb N$ and finitely supported functions $\mathbb N \to \mathbb N$. | |
| Nov 9, 2014 at 17:37 | comment | added | darij grinberg | But these Schubert polynomials aren't indexed by permutations! | |
| Nov 9, 2014 at 12:44 | history | answered | Allen Knutson | CC BY-SA 3.0 |