Related papers: Genomic Tableaux
Cylindric Young tableaux are combinatorial objects that first appeared in the 1990s. A natural extension of the classical notion of a Young tableau, they have since been used several times, most notably by Gessel and Krattenthaler and by…
We compute the generating function of column-strict plane partitions with parts in {1,2,...,n}, at most c columns, p rows of odd length and k parts equal to n. This refines both, Krattenthaler's ["The major counting of nonintersecting…
In this paper we study the orthogonality conditions satisfied by the classical q-orthogonal polynomials that are located at the top of the q-Hahn tableau (big q-jacobi polynomials (bqJ)) and the Nikiforov-Uvarov tableau (Askey-Wilson…
The paper represents three supplements to the source paper, q-bio/0610044 [q-bio.OT], with three new series of harmonic structures of the genetic code, determined by Gauss arithmetical algorithm; by Table of Minimal Adding, as in…
Standard tableaux of skew shape are fundamental objects in enumerative and algebraic combinatorics and no product formula for the number is known. In 2014, Naruse gave a formula (NHLF) as a positive sum over excited diagrams of products of…
We give a combinatorial proof of the skew Kostka analogue of the K-saturation theorem. More precisely, for any positive integer k, we give an explicit injection from the set of skew semistandard Young tableaux with skew shape…
We present families of tableaux which interpolate between the classical semi-standard Young tableaux and matching field tableaux. Algebraically, this corresponds to SAGBI bases of Pl\"ucker algebras. We show that each such family of…
We establish new explicit connections between classical (scalar) and matrix Gegenbauer polynomials, which result in new symmetries of the latter and further give access to several properties that have been out of reach before: generating…
This paper addresses the challenge of solving large-scale nonlinear equations with H\"older continuous Jacobians. We introduce a novel Incremental Gauss--Newton (IGN) method within explicit superlinear convergence rate, which outperforms…
A new generalization of Grassmannians to supergeometry, different from the well known supergrassmannian, is introduced. These are constructed by gluing a finite number of copies of a \nu\- domain, i.e. a superdomain with an odd involution,…
Weprovide an upper bound for generalized Littlewood-Richardson coefficients $c^w_{uv}$, where $u$ is a two-row Young diagram corresponding to a Grassmannian permutation. We end with a conjecture on the upper bounds for all such structure…
The relation between the Seiberg-Witten prepotentials, Nekrasov functions and matrix models is discussed. We derive quasiclassically the matrix models of Eguchi-Yang type, describing the instantonic contribution to the deformed partition…
The goal of the paper is two-fold. At first, we attempt to give a survey of some recent applications of symmetric polynomials and divided differences to intersection theory. We discuss: polynomials universally supported on degeneracy loci;…
The ring of symmetric functions occupies a central place in algebraic combinatorics, with a particularly notable role in Schubert calculus, where the standard cell decompositions of Grassmannians yield the celebrated family of Schur…
Grassmann (or anti-commuting) variables are extensively used in theoretical physics. In this paper we use Grassmann variable calculus to give new proofs of celebrated combinatorial identities such as the Lindstr\"om-Gessel-Viennot formula…
In our joint paper with W. Fulton (math.AG/9804041) we prove a formula for the cohomology class of a quiver variety. This formula involves a new class of generalized Littlewood-Richardson coefficients, all of which surprisingly seem to be…
We give an extension of the classical Schensted correspondence to the case of ribbon tableaux, where ribbons are allowed to be of different sizes. This is done by extending Fomin's growth diagram approach of the classical correspondence…
We give a new description of the Pieri rule for k-Schur functions using the Bruhat order on the affine type-A Weyl group. In doing so, we prove a new combinatorial formula for representatives of the Schubert classes for the cohomology of…
We use the theory of graph limits to study several quasi-random properties, mainly dealing with various versions of hereditary subgraph counts. The main idea is to transfer the properties of (sequences of) graphs to properties of graphons,…
Young's lattice, the lattice of all Young diagrams, has the Robinson-Schensted-Knuth correspondence, the correspondence between certain matrices and pairs of semi-standard Young tableaux with the same shape. Fomin introduced generalized…