The octahedron recurrence and RSK-correspondence
| dc.creator | Danilov, V. I. | |
| dc.creator | Koshevoy, G. A. | |
| dc.date | 2007-03-14 | |
| dc.date.accessioned | 2026-07-07T07:51:54Z | |
| dc.date.available | 2026-07-07T07:51:54Z | |
| dc.description | We start with an ``algebraic'' RSK-correspondence due to Noumi and Yamada. Given a matrix $X$, we consider a pyramidal array of solid minors of $X$. It turns out that this array satisfies an algebraic variant of octahedron recurrence. The main observation is that this array can also be constructed with the help of some square `genetic' array. Next we tropicalize this algebraic construction and consider $T$-{\em polarized} pyramidal arrays (that is arrays satisfying octahedral relations). As a result we get several bijections, viz: a) a linear bijection between non-negative arrays and supermodular functions; b) a piecewise linear bijection between supermodular functions and the so called infra-modular functions; c) a linear bijection between infra-modular functions and plane partitions. A composition of these bijections yields a bijection between non-negative arrays and plane partitions coinciding with the modified RSK-correspondence. | |
| dc.description | 16 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/math/0703414 | |
| dc.identifier | http://arxiv.org/abs/math/0703414 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125683 | |
| dc.subject | Combinatorics | |
| dc.title | The octahedron recurrence and RSK-correspondence | |
| dc.type | text |