• Corpus ID: 231741224

A New Partial Order on SYT

@inproceedings{Karaali2021ANP,
  title={A New Partial Order on SYT},
  author={Gizem Karaali and Isabella Senturia and Muge Tacskin},
  year={2021}
}
We define a new partial order on SY Tn, the set of all standard Young tableaux with n 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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TLDR
Three main results are proved: • Intervals in any of these four orders essentially describe the product in a Hopf algebra of tableaux defined by Poirier and Reutenauer, and the map sending a tableau to its descent set induces a homotopy equivalence of the proper parts of all of these orders on tableaux with that of the Boolean algebra 2[n-1].
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Let $SYT_{n}$ be the set of all standard Young tableaux with $n$ cells and $\leq_{weak}$ be Melnikov's the weak order on $SYT_n$. The aim of this paper is to introduce a conjecture, called the {\it
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Abstract This is the third paper in the series. Here we define a few combinatorial orders on Young tableaux. The first order is obtained from the induced Duflo order by the extension with the help of
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In this chapter, fundamentals of the symmetric group, namely, classes of permutations, Young diagrams, irreducible characters, and the construction of irreducible representations and their bases, are
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TLDR
The four operations defined on pairs of tableaux, linked via the involutive tableau operations of complementation and conjugation, give rise to an a priori distinct theory of dual equivalence.
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A generalized Young tableau of "shape" (pu p2, — ,Pm), where pi ^ p2 ^ i> pm ^ 1, is an array Y of positive integers yij, for 1 S j ^ Pi, 1 S i ^ m, having monotonically nondecreasing rows and
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Formulae developed to give a positive answer to Dixmier's problem for Verma and principal series submodules are used to show that each primitive ideal in the enveloping algebra of a semisimple Lie
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