Zobrazeno 1 - 10
of 12
pro vyhledávání: '"Anna Weigandt"'
Autor:
Oliver Pechenik, Anna Weigandt
Publikováno v:
Forum of Mathematics, Sigma, Vol 12 (2024)
Chow rings of flag varieties have bases of Schubert cycles $\sigma _u $ , indexed by permutations. A major problem of algebraic combinatorics is to give a positive combinatorial formula for the structure constants of this basis. The celebrated Litt
Externí odkaz:
https://doaj.org/article/545d34efb4d441dea1c17af7064700b4
Autor:
Anna Weigandt, Alexander Yong
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings, 28th... (2020)
The Schubert polynomials lift the Schur basis of symmetric polynomials into a basis for Z[x1; x2; : : :]. We suggest the prism tableau model for these polynomials. A novel aspect of this alternative to earlier results is that it directly invokes semi
Externí odkaz:
https://doaj.org/article/aa772859db9f45bda502f965c16a1042
Publikováno v:
Journal of Applied Mathematics, Vol 2010 (2010)
Optimization problems with second-order cone constraints (SOCs) can be solved efficiently by interior point methods. In order for some of these methods to get started or to converge faster, it is important to have an initial feasible point or near-fe
Externí odkaz:
https://doaj.org/article/5a874f11e18a49ccbf3294beef46aaa6
Publikováno v:
Journal of Algebra. 617:160-191
We give degree formulas for Grothendieck polynomials indexed by vexillary permutations and $1432$-avoiding permutations via tableau combinatorics. These formulas generalize a formula for degrees of symmetric Grothendieck polynomials which appeared in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::eb4b3b830ee11b1bbfc96fbb09cde6cd
https://doi.org/10.1016/j.jalgebra.2022.11.001
https://doi.org/10.1016/j.jalgebra.2022.11.001
The geometric naturality of Schubert polynomials and their combinatorial pipe dream representations was established by Knutson and Miller (2005) via antidiagonal Gr\"obner degeneration of matrix Schubert varieties. We consider instead diagonal Gr\"ob
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::09229f557ba3c697c2d24aa1e8993303
http://arxiv.org/abs/2003.13719
http://arxiv.org/abs/2003.13719
Autor:
Anna Weigandt
Publikováno v:
Algebraic Combinatorics. 1:415-423
Motivated by a recent conjecture of R. P. Stanley we offer a lower bound for the sum of the coefficients of a Schubert polynomial in terms of $132$-pattern containment.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7f11095a7d321ce127e03dd04ae55e32
https://doi.org/10.5802/alco.27
https://doi.org/10.5802/alco.27
Autor:
Anna Weigandt
Publikováno v:
Journal of Combinatorial Theory, Series A. 182:105470
In their work on the infinite flag variety, Lam, Lee, and Shimozono (2018) introduced objects called bumpless pipe dreams and used them to give a formula for double Schubert polynomials. We extend this formula to the setting of K-theory, giving an ex
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1929da733d1002f91a082ed0ea6586d5
https://doi.org/10.1016/j.jcta.2021.105470
https://doi.org/10.1016/j.jcta.2021.105470
Publikováno v:
Journal of Algebraic Combinatorics. 47:129-169
We present a particular connection between classical partition combinatorics and the theory of quiver representations. Specifically, we give a bijective proof of an analogue of A. L. Cauchy's Durfee square identity to multipartitions. We then use thi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c8efe55b84e8131a6e852eb439d2d5df
https://doi.org/10.1007/s10801-017-0771-5
https://doi.org/10.1007/s10801-017-0771-5
We give an explicit formula for the degree of the Grothendieck polynomial of a Grassmannian permutation and a closely related formula for the Castelnuovo-Mumford regularity of the Schubert determinantal ideal of a Grassmannian permutation. We then pr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f49829210630ff4616ac2a251a27d390
http://arxiv.org/abs/1912.04477
http://arxiv.org/abs/1912.04477
We study the action of a differential operator on Schubert polynomials. Using this action, we first give a short new proof of an identity of I. Macdonald (1991). We then prove a determinant conjecture of R. Stanley (2017). This conjecture implies the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1b1ef87c1e1185539dec0f738e28665e
http://arxiv.org/abs/1812.00321
http://arxiv.org/abs/1812.00321