From generalized permutahedra to Grothendieck polynomials via flow polytopes

Karola Mészáros, Avery St. Dizier
<span title="2020-10-12">2020</span> <i title="Cellule MathDoc/CEDRAM"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jtld4aoak5ayfhb6qq4ltptrmi" style="color: black;">Algebraic Combinatorics</a> </i> &nbsp;
We study a family of dissections of flow polytopes arising from the subdivision algebra. To each dissection of a flow polytope, we associate a polynomial, called the left-degree polynomial, which we show is invariant of the dissection considered (proven independently by Grinberg). We prove that left-degree polynomials encode integer points of generalized permutahedra. Using that certain left-degree polynomials are related to Grothendieck polynomials, we resolve special cases of conjectures by
more &raquo; ... nical, Tokcan, and Yong regarding the saturated Newton polytope property of Grothendieck polynomials.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5802/alco.136">doi:10.5802/alco.136</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/q2c56txehjgedgm66zh3g5myly">fatcat:q2c56txehjgedgm66zh3g5myly</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201214001045/https://alco.centre-mersenne.org/article/ALCO_2020__3_5_1197_0.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/eb/17/eb173a1a9a0b980fcc5932090767f7e91dcf043a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5802/alco.136"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>