Zobrazeno 1 - 10
of 17
pro vyhledávání: '"Zachary Hamaker"'
Autor:
Zachary Hamaker, Nathan Williams
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings, 27th..., Iss Proceedings (2015)
Using the powerful machinery available for reduced words of type $B$, we demonstrate a bijection between centrally symmetric $k$-triangulations of a $2(n + k)$-gon and plane partitions of height at most $k$ in a square of size $n$. This bijection can
Externí odkaz:
https://doaj.org/article/c0c8a61222b547f08733819381b2ea92
Autor:
Zachary Hamaker, Benjamin Young
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AS,..., Iss Proceedings (2013)
The Little map and the Edelman-Greene insertion algorithm, a generalization of the Robinson-Schensted correspondence, are both used for enumerating the reduced decompositions of an element of the symmetric group. We show the Little map factors throug
Externí odkaz:
https://doaj.org/article/243234c4488a46bb9f40a474276acec5
Publikováno v:
Canadian Journal of Mathematics. 74:1310-1346
Involution Schubert polynomials represent cohomology classes of $K$-orbit closures in the complete flag variety, where $K$ is the orthogonal or symplectic group. We show they also represent $T$-equivariant cohomology classes of subvarieties defined b
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::78b7c5b59a3b3e8a39406d43a634ca08
https://doi.org/10.4153/s0008414x21000274
https://doi.org/10.4153/s0008414x21000274
Publikováno v:
Algebraic Combinatorics. 3:365-388
Given a set of permutations Pi, let S_n(Pi) denote the set of permutations in the symmetric group S_n that avoid every element of Pi in the sense of pattern avoidance. Given a subset S of {1,...,n-1}, let F_S be the fundamental quasisymmetric functio
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::650f800a90e7f92b72af1363f1ee562d
https://doi.org/10.5802/alco.96
https://doi.org/10.5802/alco.96
Autor:
Michael Coopman, Zachary Hamaker
In this note, we introduce a statistic on Motzkin paths that describes the rank generating function of Bruhat order for involutions. Our proof relies on a bijection introduced by Philippe Biane from permutations to certain labeled Motzkin paths and a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::319794d78fae6f12a5c6fe8a146dace3
http://arxiv.org/abs/2106.06021
http://arxiv.org/abs/2106.06021
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
Publikováno v:
International Mathematics Research Notices. 2019:5389-5440
The involution Stanley symmetric functions $\hat{F}_y$ are the stable limits of the analogues of Schubert polynomials for the orbits of the orthogonal group in the flag variety. These symmetric functions are also generating functions for involution w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b0d05c7498e902a8bcb10549038b87fc
https://doi.org/10.1093/imrn/rnx274
https://doi.org/10.1093/imrn/rnx274
Autor:
Victor Reiner, Zachary Hamaker
Publikováno v:
European Journal of Combinatorics. 86:103083
Monotone triangles are a rich extension of permutations that biject with alternating sign matrices. The notions of weak order and descent sets for permutations are generalized here to monotone triangles, and shown to enjoy many analogous properties.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a25684a7a688222d498b324824fbe99c
https://doi.org/10.1016/j.ejc.2020.103083
https://doi.org/10.1016/j.ejc.2020.103083
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
The orbits of the symplectic group acting on the type A flag variety are indexed by the fixed-point-free involutions in a finite symmetric group. The cohomology classes of the closures of these orbits have polynomial representatives $\hat{\mathfrak{S
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fb6a18e079ea3b34d7ff4916828c14ab
http://arxiv.org/abs/1706.06665
http://arxiv.org/abs/1706.06665