Related papers: Cylindric skew Schur functions

An expression of the multivariate sigma function associated with a (n,s)-curve is given in terms of algebraic integrals. As a corollary the first term of the series expansion around the origin of the sigma function is directly proved to be…

In this paper, we study Grothendieck polynomials from a combinatorial viewpoint. We introduce the factorial Grothendieck polynomials, analogues of the factorial Schur functions and present some of their properties, and use them to produce a…

We investigate a generalization of the classical notion of a Schur functor associated to a ribbon diagram. These functors are defined with respect to an arbitrary algebra, and in the case that the underlying algebra is the…

Lam and Pylyavskyy introduced loop symmetric functions as a generalization of symmetric functions. They defined loop Schur functions as generating functions over semistandard tableaux with respect to a `colored weight,' and they proved a…

For $k\ge 1$, the homogeneous symmetric functions $G(k,m)$ of degree $m$ defined by $\sum_{m\ge 0} G(k,m) z^m=\prod_{i\ge 1} \big(1+x_iz+x^2_iz^2+\cdots+x^{k-1}_iz^{k-1}\big)$ are called \emph{Petrie symmetric functions}. As derived by…

While equality of skew Schur functions is well understood, the problem of determining when two skew Schur $Q$ functions are equal is still largely open. It has been studied in the case of ribbon shapes in 2008 by Barekat and van…

For a skew shape $\lambda/\mu$, we define the hybrid Grothendieck polynomial $${G}_{\lambda/\mu}(\textbf{x};\textbf{t};\textbf{w}) =\sum_{T\in \mathrm{SVRPP}(\lambda/\mu)} \textbf{x}^{\mathrm{ircont}(T)}\textbf{t}^{\mathrm{ceq}…

The symmetric Grothendieck polynomials generalize Schur polynomials and are Schur-positive by degree. Combinatorially this is manifested as the generalization of semistandard Young tableaux by set-valued tableaux. We define a (weak)…

In this paper we would like to show the interrelation between the different mathematical theories concerning the Schur interpolation problem, contractions in Hilbert spaces, pseudocontinuation and Darlington synthesis. The main objects of…

We present an axiomatic frame (in Prt I of this book) in which many results of the K-theory for C*-algebras are proved. Then we construct an example for this axiomatic theory (in Part II), which generalizes the classical theory for…

We describe a combinatorial formula for the coefficients when the dual immaculate quasisymmetric functions are decomposed into Young quasisymmetric Schur functions. We prove this using an analogue of Schensted insertion. Using this result,…

Introduced by Okounkov and Reshetikhin, the Schur process is known to be a determinantal point process, meaning that its correlation functions are minors of a single correlation kernel matrix. Previously, this was derived using…

We study three-dimensional partition functions constructed from the tetrahedral $L$-operator introduced and studied by Bazhanov-Sergeev and Kuniba-Maruyama-Okado. First, we explore the $q=0$ case, extending the authors' previous results and…

Three decades ago, Stanley and Brenti initiated the study of the Kazhdan--Lusztig--Stanley (KLS) functions, putting on common ground several polynomials appearing in algebraic combinatorics, discrete geometry, and representation theory. In…

We obtain a new formula to relate the value of a Schur polynomial with variables $(x_1,\ldots,x_N)$ with values of Schur polynomials at $(1,\ldots,1)$. This allows to study the limit shape of perfect matchings on a square hexagon lattice…

We find a simple criterion for the equality $Q_\lambda=Q_{\mu/\nu}$ where $Q_\lambda$ and $Q_{\mu/\nu}$ are Schur's Q-functions on infinitely many variables.

We find closed-form expressions for the Schur indices of 4d $\mathcal{N}=2^{*}$ super Yang-Mills theory with unitary gauge groups for arbitrary ranks via the Fermi-gas formulation. They can be written as a sum over the Young diagrams…

We show that normalized Schur polynomials are strongly log-concave. As a consequence, we obtain Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients in the special case of Kostka numbers.

In this paper we prove a quaternionic positive real lemma as well as its generalized version, in case the associated kernel has negative squares for slice hyperholomorphic functions. We consider the case of functions with positive real part…

Using symmetric function theory, we study the cycle structure and increasing subsequence structure of permutations after various shuffling methods, emphasizing the role of Cauchy type identities and the Robinson-Schensted-Knuth…