Related papers: Standard Rothe Tableaux
For each permutation $w$, we can construct a collection of hyperplanes $\mathcal{A}_w$ according to the inversions of $w$, which is called the inversion hyperplane arrangement associated to $w$. It was conjectured by Postnikov and confirmed…
This work is concerned with some properties of the Young-Fibonacci insertion algorithm and its relation with Fomin's growth diagrams. It also investigates a relation between the combinatorics of Young-Fibonacci tableaux and the study of…
We present a bijection between vacillating tableaux and pairs consisting of a standard Young tableau and an orthogonal Littlewood-Richardson tableau for the special orthogonal group $\mathrm{SO}(2k+1)$. This bijection is motivated by the…
Linked partitions are introduced by Dykema in the study of transforms in free probability theory, whereas permutation tableaux are introduced by Steingr\'{i}msson and Williams in the study of totally positive Grassmannian cells. Let…
A cyclic descent function on standard Young tableaux of size $n$ is a function that restricts to the usual descent function when $n$ is omitted, such that the number of standard Young tableaux of given shape with cyclic descent set…
The right key of a semistandard Young tableau is a tool used to find Demazure characters for $sl_n(\mathbb{C})$. This thesis gives methods to obtain the right and left keys by inspection of the semistandard Young tableau. Given a partition…
We study three aspects of commutation classes of reduced decompositions: the number of commutation classes, the structures of their corresponding graphs, and the enumeration of subnetworks, a concept recently introduced by Warrington [21].…
Let $w$ be a permutation of $\{1,2,\ldots,n \}$, and let $D(w)$ be the Rothe diagram of $w$. The Schubert polynomial $\mathfrak{S}_w(x)$ can be realized as the dual character of the flagged Weyl module associated to $D(w)$. This implies a…
Arc permutations and unimodal permutations were introduced in the study of triangulations and characters. This paper studies combinatorial properties and structures on these permutations. First, both sets are characterized by pattern…
In this paper, explicit formulae for the expectation and the variance of descent functions on random standard Young tableaux are presented. Using these, it is shown that the normalized variance, $V/E^2$, is bounded if and only if a certain…
Let the sign of a standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. A conjecture by Richard Stanley says that the sum of the signs of all SYTs with n squares is 2^[n/2].…
Walks on Young's lattice of integer partitions encode many objects of algebraic and combinatorial interest. Chen et al. established connections between such walks and arc diagrams. We show that walks that start at $\varnothing$, end at a…
We present bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (2+2)-free posets and a certain class of involutions (or chord diagrams), already appeared in the literature, but were apparently not…
We develop a notion of a dual of a graph, generalizing the definition of Goulden and Yong (which only applied to trees), and reproving their main result using our new notion. We in fact give three definitions of the dual: a graph-theoretic…
A permutation graph is a graph whose edges are given by inversions of a permutation. We study the Abelian sandpile model (ASM) on such graphs. We exhibit a bijection between recurrent configurations of the ASM on permutation graphs and the…
Given a Stirling permutation w, we introduce the mesa set of w as the natural generalization of the pinnacle set of a permutation. Our main results characterize admissible mesa sets and give closed enumerative formulas in terms of rational…
We consider a new kind of straight and shifted plane partitions/Young tableaux --- ones whose diagrams are no longer of partition shape, but rather Young diagrams with boxes erased from their upper right ends. We find formulas for the…
Inspired by a width invariant on permutations defined by Guillemot and Marx, Bonnet, Kim, Thomass\'e, and Watrigant introduced the twin-width of graphs, which is a parameter describing its structural complexity. This invariant has been…
The number of standard Young tableaux of a skew shape $\lambda/\mu$ can be computed as a sum over excited diagrams inside $\lambda$. Excited diagrams are in bijection with certain lozenge tilings, with flagged semistandard tableaux and also…
In recent work of Baik, Deift and Rains convergence of moments was established for the limiting joint distribution of the lengths of the first k rows in random Young tableaux. The main difficulty was obtaining a good estimate for the tail…