Zobrazeno 1 - 10
of 468
pro vyhledávání: '"Frank Sottile"'
Publikováno v:
Journal of Software for Algebra and Geometry. 11:53-59
The Macaulay2 package DecomposableSparseSystems implements methods for studying and numerically solving decomposable sparse polynomial systems. We describe the structure of decomposable sparse systems and explain how the methods in this package may b
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::df8173c500512c630d3ea317dde229bb
https://doi.org/10.2140/jsag.2021.11.53
https://doi.org/10.2140/jsag.2021.11.53
Publikováno v:
Arnold Mathematical Journal.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5917330bbf923b3df7b94f190694cb82
https://doi.org/10.1007/s40598-022-00221-2
https://doi.org/10.1007/s40598-022-00221-2
Publikováno v:
Mathematics of Computation. 90:1407-1433
We develop the Littlewood-Richardson homotopy algorithm, which uses numerical continuation to compute solutions to Schubert problems on Grassmannians and is based on the geometric Littlewood-Richardson rule. One key ingredient of this algorithm is ou
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::117d8af55347cccab9b061ff1b3e994e
https://doi.org/10.1090/mcom/3579
https://doi.org/10.1090/mcom/3579
Publikováno v:
Linear Algebra and its Applications. 610:488-505
Typically, a linear projection of the Grassmannian in its Plucker embedding is generically injective, unless the image of the Grassmannian is a linear space. A notable exception are self-adjoint linear projections, which have even degree. We consider
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c0523ed9d5255e2a9f4d4d1547b31c0a
https://doi.org/10.1016/j.laa.2020.10.006
https://doi.org/10.1016/j.laa.2020.10.006
Publikováno v:
Forum Mathematicum. 31:779-783
We use geometry to give a short proof of an equivariant Pieri rule in the classical flag manifold. This rule is due to Robinson, who gave an algebraic proof.
6 pages
6 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::55e9fbf13eb458e769c3c4a442ca72f3
https://doi.org/10.1515/forum-2018-0213
https://doi.org/10.1515/forum-2018-0213
Autor:
Frank Sottile
Publikováno v:
ISSAC
Numerical algebraic geometry has a close relationship to intersection theory from algebraic geometry. We deepen this relationship, explaining how rational or algebraic equivalence gives a homotopy. We present a general notion of witness set for subva
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dec27f328d79c7b87b96f528fb7369c9
http://arxiv.org/abs/2002.00180
http://arxiv.org/abs/2002.00180
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AR,..., Iss Proceedings (2012)
We show that the Galois group of any Schubert problem involving lines in projective space contains the alternating group. Using a criterion of Vakil and a special position argument due to Schubert, this follows from a particular inequality among Kost
Externí odkaz:
https://doaj.org/article/debd78bfcfce45ad920d5125c7d4794b
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AO,..., Iss Proceedings (2011)
We develop the notion of the composition of two coalgebras, which arises naturally in higher category theory and the theory of species. We prove that the composition of two cofree coalgebras is cofree and give conditions which imply that the composit
Externí odkaz:
https://doaj.org/article/62de500c583c40d9b84ffc9808e25c4d
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AK,..., Iss Proceedings (2009)
The multiplihedra $\mathcal{M}_{\bullet} = (\mathcal{M}_n)_{n \geq 1}$ form a family of polytopes originating in the study of higher categories and homotopy theory. While the multiplihedra may be unfamiliar to the algebraic combinatorics community, i
Externí odkaz:
https://doaj.org/article/6a53d23481a04bfe84aa792ce47e6f42