A New Partial Order on SYT
Gizem Karaali, Isabella Senturia, M\"uge Ta\c{s}kin
TL;DR
This paper introduces a novel partial order on the set of standard Young tableaux by integrating chain order with horizontal strips, and explores its key properties.
Contribution
It presents a new partial order on SYT that combines existing concepts and establishes its fundamental properties.
Findings
The new order is well-defined and exhibits desirable mathematical properties.
It unifies chain order and horizontal strip concepts in SYT.
The order has potential applications in combinatorics and representation theory.
Abstract
We define a new partial order on , the set of all standard Young tableaux with cells, by combining the chain order with the notion of horizontal strips. We prove various desirable properties of this new order.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Random Matrices and Applications