Related papers: Folding rotationally symmetrical tableaux via webs
We show that Sch\"utzenberger's promotion on two and three row rectangular Young tableaux can be realized as cyclic rotation of certain planar graphs introduced by Kuperberg. Moreover, following work of the third author, we show that this…
We consider domino tilings of three-dimensional cubiculated regions. A flip is a local move: two neighboring parallel dominoes are removed and placed back in a different position. The twist is an integer associated to each tiling, which is…
A tableau inversion is a pair of entries from the same column of a row-standard tableau that lack the relative ordering necessary to make the tableau column-standard. An $i$-inverted Young tableau is a row-standard tableau with precisely…
In this paper, we consider the set of all domino tilings of a cubiculated region. The primary question we explore is: How can we move from one tiling to another? Tiling spaces can be viewed as spaces of subgraphs of a fixed graph with a…
We define mosaics, which are naturally in bijection with Knutson-Tao puzzles. We define an operation on mosaics, which shows they are also in bijection with Littlewood-Richardson skew-tableaux. Another consequence of this construction is…
In contrast to many known results concerning periodic tilings of the Euclidean plane with pentagons, here tilings with rotational symmetry are investigated. A certain class of convex pentagons is introduced. It can be shown that for any…
Regarding the Specht modules associated to the two-row partition $(n,n)$, we provide a combinatorial path model to study the transitioning matrix from the tableau basis to the $A_1$-web basis (i.e. cup diagrams), and prove that the entries…
Scaffolds are certain tensors arising in the study of association schemes, and have been (implicitly) understood diagrammatically as digraphs with distinguished "root" nodes and with matrix edge weights, often taken from Bose-Mesner…
We consider three-dimensional domino tilings of cylinders $\mathcal{R}_N = \mathcal{D} \times [0,N]$ where $\mathcal{D} \subset \mathbb{R}^2$ is a fixed quadriculated disk and $N \in \mathbb{N}$. A domino is a $2 \times 1 \times 1$ brick. A…
Self-folding is an emerging paradigm for the inverse design of three-dimensional structures. While most efforts have concentrated on the shape of the net, our approach introduces a new design dimension-bond specificity between the edges. We…
We examine domino tilings of rectangular boards, which are in natural bijection with perfect matchings of grid graphs. This leads to the study of their associated perfect matching polytopes, and we present some of their properties, in…
We study vectors formed by entries on the diagonal of standard Young tableaux of shifted shapes. Such vectors are in bijection with integer lattice points of certain integral polytopes, which are Minkowski sums of simplices. We also…
Many real-world applications require aligning two temporal sequences, including bioinformatics, handwriting recognition, activity recognition, and human-robot coordination. Dynamic Time Warping (DTW) is a popular alignment method, but can…
We introduce the notion of a generalized oscillating tableau and define a promotion operation on such tableaux that generalizes the classical promotion operation on standard Young tableaux. As our main application, we show that this…
This paper investigates flat webs on the projective plane. We present two methods for constructing such webs: the first involves taking the product of finitely many convex reduced foliations and invariant lines, while the second consists of…
The number of standard Young tableaux of a fixed shape is famously given by the hook-length formula due to Frame, Robinson and Thrall. A bijective proof of Novelli, Pak and Stoyanovskii relies on a sorting algorithm akin to jeu-de-taquin…
The present paper deals with the discrete inverse problem of reconstructing binary matrices from their row and column sums under additional constraints on the number and pattern of entries in specified minors. While the classical…
Two-dimensional mirror symmetry enriched topological (SET) orders can be studied using the folding approach: it can be folded along the mirror axis and turned into a bilayer system on which the mirror symmetry acts as a $\mathbb Z_2$…
We study various duality webs involving the 3d FT[SU(N)] theory, a close relative of the T[SU(N)] quiver tail. We first map the partition functions of FT[SU(N)] and its 3d spectral dual to a pair of spectral dual q-Toda conformal blocks.…
We study the number of tilings of skew Young diagrams by ribbon tiles shaped like Dyck paths, in which the tiles are "vertically decreasing". We use these quantities to compute pairing probabilities in the double-dimer model: Given a planar…