Related papers: Hook formulas for skew shapes II. Combinatorial pr…

We produce a new basis for the Schur and Weyl modules associated to a row-convex shape, D. The basis is indexed by new class of "straight" tableaux which we introduce by weakening the usual requirements for standard tableaux. Spanning is…

We develop a calculus for diagrams of knotted objects. We define Arrow presentations, which encode the crossing informations of a diagram into arrows in a way somewhat similar to Gauss diagrams, and more generally w-tree presentations,…

We provide the special values of the skew version of the $K$-theoretic Schur $P$- and $Q$-functions. Using these special values, we show an oddness property of the number of shifted set-valued skew tableaux. Additionally, we generalize…

New sufficient conditions and necessary conditions are developed for two skew diagrams to give rise to the same skew Schur function. The sufficient conditions come from a variety of new operations related to ribbons (also known as border…

Using lattice path counting arguments, we reproduce a well known formula for the number of standard Young tableaux. We also produce an interesting new formula for tableaux of height $\leq 3$ using the Fourier methods of Ault and Kicey.

We show that sequences of skew Schur polynomials obtained from stretched semi-standard Young tableaux satisfy a linear recurrence, which we give explicitly. Using this, we apply this to finding certain asymptotic behavior of these Schur…

We define the slant sum of quiver gauge theories, a gluing on the underlying quivers that identifies a gauge vertex with a framing vertex. Under some mild assumptions, we relate torus fixed points on the corresponding Higgs branches, which…

We consider the skew Howe duality for the action of certain dual pairs of Lie groups $(G_1, G_2)$ on the exterior algebra $\bigwedge(\mathbb{C}^{n} \otimes \mathbb{C}^{k})$ as a probability measure on Young diagrams by the decomposition…

For every connected graph $G$ and surface $S$, we consider the well-known string of inequalities $\delta_S(G) \leq \mu_S(G) \leq \nu_S(G)$, where $\mu$ and $\nu$ denote skewness and crossing number and $\delta$ is the Euler-formula lower…

Several hook summation formulae for binary trees have appeared recently in the literature. In this paper we present an analogous formula for unordered increasing trees of size r, which involves r parameters. The right-hand side can be…

In this paper we describe the thickened strips and the outside nested decompositions of any skew shape $\lambda/\mu$. For any such decomposition $\Phi=(\Theta_1,\Theta_2,\ldots,\Theta_g)$ of the skew shape $\lambda/\mu$ where $\Theta_i$ is…

We give a counting formula for the set of rectangular increasing tableaux in terms of generalized Narayana numbers. We define small $m$-Schr\"oder paths and give a bijection between the set of increasing rectangular tableaux and small…

The variety of skew braces contains several interesting subcategories as subvarieties, as for instance the varieties of radical rings, of groups and of abelian groups. In this article the methods of non-abelian homological algebra are…

The skew Schubert polynomials are those which are indexed by skew elements of the Weyl group, in the sense of arXiv:0812.0639. We obtain tableau formulas for the double versions of these polynomials in all four classical Lie types, where…

We study the Pieri type formulas for the Schur multiple zeta functions along with those for the Schur polynomials. To formulate these formulas, we introduce a new insertion rule for adding boxes in the Young tableaux and obtain the results…

The purpose of this note is to prove an Euler-type formula for partitions of the M\"obius strip. This formula was introduced in our joint paper with R.~Kiwan, "Courant-sharp property for Dirichlet eigenfunctions on the M\"obius strip"…

Recently, Han obtained two hook length formulas for binary trees and asked for combinatorial proofs. One of Han's formulas has been generalized to k-ary trees by Yang. Sagan has found a probabilistic proof of Yang's extension. We give…

We compute the Schur indices in the presence of some line operators based on our con- jectural formula introduced in [1]. In particular, we focus on the rank 1 superconformal field theories with the enhanced global symmetry and the free…

Spline functions have long been used in numerical solution of differential equations. Recently it revives as isogeometric analysis, which offers integration of finite element analysis and NURBS based CAD into a single unified process.…

We give a combinatorial expansion of the stable Grothendieck polynomials of skew Young diagrams in terms of skew Schur functions, using a new row insertion algorithm for set-valued semistandard tableaux of skew shape. This expansion unifies…