Fetching the paper…

Reading the bibliography…

2014

Schubert calculus and shifting of interval positroid varieties

Knutson, Allen

Original
PDF
Post on X

Understand

Consider k x n matrices with rank conditions placed on intervals of columns.

The ranks that are actually achievable correspond naturally to upper triangular partial permutation matrices, and we call the corresponding subvarieties of Gr(k,n) the _interval positroid varieties_, as this class lies within the class of positroid varieties studied in [Knutson-Lam-Speyer].
It includes Schubert and opposite Schubert varieties, and their intersections, and is Grassmann dual to the projection varieties of [Billey-Coskun].
Vakil's "geometric Littlewood-Richardson rule" [Vakil] uses certain degenerations to positively compute the H^*-classes of Richardson varieties, each summand recorded as a (2+1)-dimensional "checker game".

Schubert calculus and shifting of interval positroid varieties · Around

Built on

Pál Erdős, Chao Ko, Richard Rado:
1961
Earlier work this paper cites.
Neil White:
1975
Earlier work this paper cites.
Andrzej Białynicki-Birula:
1976
Earlier work this paper cites.
Peter Frankl:
1987
Earlier work this paper cites.
William Fulton:
1992
Earlier work this paper cites.
William Graham:
2001
Earlier work this paper cites.
Michel Brion:
2002
Earlier work this paper cites.

Similar

Gil Kalai:
2002
Cited alongside, same era.
by same author, Terence Tao:
2003
Cited alongside, same era.
Thomas Lam, Mark Shimozono:
2005
Cited alongside, same era.
Ravi Vakil:
2006
Cited alongside, same era.
Joseph Bonin, Anna de Mier:
2008
Cited alongside, same era.
Allen Knutson, Ezra Miller, Alex Yong:
2009
Cited alongside, same era.
Sami Assaf, Nantel Bergeron, Frank Sottile:
Cited in the paper.
Alexandre Borovik, Israel Gelfand, Neil White:
Cited in the paper.
Nicolas Ford, David Speyer:
Cited in the paper.
Xuhua He, Thomas Lam:
Original
Cited in the paper.
by same author:
Original
Cited in the paper.
by same author, Mathias Lederer:
Cited in the paper.

Then

Paul Zinn-Justin:
Original
2009
Later among the works it cites.
David Anderson, Stephen Griffeth, Ezra Miller:
Original
2011
Later among the works it cites.
Sara Billey, Izzet Co skun:
Original
2012
Later among the works it cites.
by same author, T. Lam, D. Speyer:
Original
2013
Later among the works it cites.
by same author, Thomas Lam, David Speyer:
Original
2014
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Karóla Mészáros, Greta Panova, Alex Postnikov:

2014

Closest in time.