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Edge vectors on plabic networks in the disk and amalgamation of totally non-negative Grassmanniansстатья
Статья опубликована в высокорейтинговом журнале
Информация о цитировании статьи получена из
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 13 июля 2022 г.
- Авторы: Abenda Simonetta, Grinevich Petr G.
- Журнал: Advances in Mathematics
- Том: 406
- Год издания: 2022
- Издательство: Academic Press
- Местоположение издательства: United States
- Первая страница: 108523
- DOI: 10.1016/j.aim.2022.108523
- Аннотация: The principal result is the enrichment of Postnikov's construction by associating measurements not only to boundary edges or vertices, but to internal edges as well. Indeed we generalize prior results by Postnikov and Talaska providing an explicit representation of the solution to the system of geometric relations on the network of graph G and positive weights. At this aim, we assign canonical basis vectors in at the boundary sinks and define the vectors components at the edge e as (finite or infinite) summations over the directed paths from e to the given boundary sink. Such edge vectors have the following properties: 1) They solve the geometric system of relations on this network; 2) Their components are rational in the weights with subtraction–free denominators, and have explicit expressions in terms of the conservative and edge flows of. At the boundary sources they coincide with the entries of the boundary measurement matrix defined in. If the graph is acyclically orientable, all components are subtraction–free rational expressions in the weights with respect to a convenient basis. Null edge vectors may occur on reducible networks not acyclically orientable; 3) We provide explicit formulas both for the transformation rules of the edge vectors with respect to the orientation and the several gauges of the given network, and for their transformations due to moves and reductions of networks.
- Добавил в систему: Гриневич Петр Георгиевич