Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMinimal Bar Tableaux
377
0
0.0
(
0
)
Authors
Peter Clifford
Ask ChatGPT about the research
No Arabic abstract
Motivated by Stanleys results in cite{St02}, we generalize the rank of a partition $lambda$ to the rank of a shifted partition $S(lambda)$. We show that the number of bars required in a minimal bar tableau of $S(lambda)$ is max$(o, e + (ell(lambda) mathrm{mod} 2))$, where $o$ and $e$ are the number of odd and even rows of $lambda$. As a consequence we show that the irreducible projective characters of $S_n$ vanish on certain conjugacy classes. Another corollary is a lower bound on the degree of the terms in the expansion of Schurs $Q_{lambda}$ symmetric functions in terms of the power sum symmetric functions.
rate research
Read More
In 1976, King defined certain tableaux model, called King tableaux in this paper, counting weight multiplicities of irreducible representation of the symplectic group $Sp(2m)$ for a given dominant weight. Since Kashiwara defined crystals, it is an open problem to provide a crystal structure on King tableaux. In this paper, we present crystal structures on King tableaux and semistandard oscillating tableaux. The semistandard oscillating tableaux naturally appear as $Q$-tableaux in the symplectic version of RSK algorithms. As an application, we discuss Littlewood-Richardson coefficients for $Sp(2m)$ in terms of semistandard oscillating tableaux.
This paper completely characterizes the standard Young tableaux that can be reconstructed from their sets or multisets of $1$-minors. In particular, any standard Young tableau with at least $5$ entries can be reconstructed from its set of $1$-minors.
We give a counting formula for the set of rectangular increasing tableaux in terms of generalized Narayana numbers. We define small $m$-Schroder paths and give a bijection between the set of increasing rectangular tableaux and small $m$-Schroder paths, generalizing a result of Pechenik [3]. Using $K$-jeu de taquin promotion, which was defined by Thomas and Yong [10], we give a cyclic sieving phenomenon for the set of increasing hook tableaux.
In this paper, we propose a notion of colored Motzkin paths and establish a bijection between the $n$-cell standard Young tableaux (SYT) of bounded height and the colored Motzkin paths of length $n$. This result not only gives a lattice path interpretation of the standard Young tableaux but also reveals an unexpected intrinsic relation between the set of SYTs with at most $2d+1$ rows and the set of SYTs with at most 2d rows.
In this paper, we study a new cyclic sieving phenomenon on the set $mathsf{SST}_n(lambda)$ of semistandard Young tableaux with the cyclic action $mathsf{c}$ arising from its $U_q(mathfrak{sl}_n)$-crystal structure. We prove that if $lambda$ is a Young diagram with $ell(lambda) < n$ and $gcd( n, |lambda| )=1$, then the triple $left( mathsf{SST}_n(lambda), mathsf{C}, q^{- kappa(lambda)} s_lambda(1,q, ldots, q^{n-1}) right) $ exhibits the cyclic sieving phenomenon, where $mathsf{C}$ is the cyclic group generated by $mathsf{c}$. We further investigate a connection between $mathsf{c}$ and the promotion $mathsf{pr}$ and show the bicyclic sieving phenomenon given by $mathsf{c}$ and $mathsf{pr}^n$ for hook shape.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
