Related papers: Outside nested decompositions of skew diagrams and…

A decomposition of a multigraph $G$ is a partition of its edges into subgraphs $G(1), \ldots , G(k)$. It is called an $r$-factorization if every $G(i)$ is $r$-regular and spanning. If $G$ is a subgraph of $H$, a decomposition of $G$ is said…

Arnold, Falk, & Winther, in "Finite element exterior calculus, homological techniques, and applications" (2006), show how to geometrically decompose the full and trimmed polynomial spaces on simplicial elements into direct sums of…

In this paper we prove the case $dim(V_3)=3$ of a conjecture about the exterior operad ${\Lambda}^{S^2}_{V_d}$. For this we introduce a collection of natural involutions on the set of homogeneous cycle-free $d$-partitions of the complete…

This work highlights the existence of partial symmetries in large families of iterated plethystic coefficients. The plethystic coefficients involved come from the expansion in the Schur basis of iterated plethysms of Schur functions indexed…

The Naruse hook-length formula is a recent general formula for the number of standard Young tableaux of skew shapes, given as a positive sum over excited diagrams of products of hook-lengths. In 2015 we gave two different $q$-analogues of…

Length-constrained expander decompositions are a new graph decomposition that has led to several recent breakthroughs in fast graph algorithms. Roughly, an $(h, s)$-length $\phi$-expander decomposition is a small collection of length…

Let $k$, $\lambda$ and $\mu$ be positive integers. A decomposition of a multigraph $ \lambda G$ into edge-disjoint subgraphs $G_1, \ldots , G_k$ is said to be \emph{enclosed} by a decomposition of a multigraph $\mu H$ into edge-disjoint…

Suppose $\mu$ is a partition of $n$ and $\lambda$ a composition of $n$, and let $S^\mu$, $M^\lambda$ denote the Specht module and permutation module defined by Dipper and James for the Iwahori--Hecke algebra $\mathscr{H}_n$ of the symmetric…

The plethysm product of Schur functions corresponds to composing polynomial representations of infinite general linear groups. Finding the plethysm coefficients $\langle s_\nu \circ s_\mu, s_\lambda\rangle$ that express an arbitrary…

The Schur polynomials $s_{\lambda}$ are essential in understanding the representation theory of the general linear group. They also describe the cohomology ring of the Grassmannians. For $\rho = (n, n-1, \dots, 1)$ a staircase shape and…

The spectral decomposition of the path space of the vertex model associated to the level $l$ representation of the quantized affine algebra $U_q(\hat{sl}_n)$ is studied. The spectrum and its degeneracy are parametrized by skew Young…

An element [\Phi] of the Grassmannian of n-dimensional subspaces of the Hardy space H^2, extended over the field C(x_1,..., x_n), may be associated to any polynomial basis {\phi} for C(x). The Pl\"ucker coordinates…

We define a graded graph, called the Schur--Weyl graph, which arises naturally when one considers simultaneously the RSK algorithm and the classical duality between representations of the symmetric and general linear groups. As one of the…

The Hecke algebra H_n contains well known idempotents E_{\lambda} which are indexed by Young diagrams with n cells. They were originally described by Gyoja. A skein theoretical description of E_{\lambda} was given by Aiston and Morton. The…

We study multiplication of any Schubert polynomial $\mathfrak{S}_w$ by a Schur polynomial $s_\lambda$ (the Schubert polynomial of a Grassmannian permutation) and the expansion of this product in the ring of Schubert polynomials. We derive…

We revisit a double-scaled limit of the superconformal index of ${\cal N}=2$ superconformal field theories (SCFTs) which generalizes the Schur index. The resulting partition function, $\hat {\cal Z}(q,\alpha)$, has a standard $q$-expansion…

Tutte's spring embedding theorem states that, for a three-connected planar graph, if the outer face of the graph is fixed as the complement of some convex region in the plane, and all other vertices are placed at the mass center of their…

The ideal (tagged resp.) triangulation of bounded surface with marked points are associated with skew-symmetric (skew-symmetrizable) exchange matrices. An algo- rithm is established to decompose the graph associated to such matrix. There…

We give a new interpretation of the shifted Littlewood-Richardson coefficients $f_{\lambda\mu}^\nu$ ($\lambda,\mu,\nu$ are strict partitions). The coefficients $g_{\lambda\mu}$ which appear in the decomposition of Schur $Q$-function…

We introduce two new bases of QSym, the flipped extended Schur functions and the backward extended Schur functions, as well as their duals in NSym, the flipped shin functions and the backward shin functions. These bases are the images of…