Related papers: Enumeration of bounded lecture hall tableaux
We express the topological expansion of the Jacobi Unitary Ensemble in terms of triple monotone Hurwitz numbers. This completes the combinatorial interpretation of the topological expansion of the classical unitary invariant matrix…
In this paper, we firstly extend a result of Bonin, Shapiro and Simion by giving the distribution of the major index over generalized Schr\"{o}der paths. Then by providing a bijection between generalized Schr\"{o}der paths and…
We give a Hecke algebra derivation of Macdonald's expansion formula for Hall-Littlewood polynomials in terms of semistandard Young tableaux. This is accomplished by first obtaining a Hecke algebra lift of the expansion coefficients and then…
We explain connections among several, a priori unrelated, areas of mathematics: combinatorics, algebraic statistics, topology and enumerative algebraic geometry. Our focus is on discrete invariants, strongly related to the theory of…
Lattice paths effectively model phenomena in chemistry, physics and probability theory. Asymptotic enumeration of lattice paths is linked with entropy in the physical systems being modeled. Lattice paths restricted to different regions of…
We introduce a new combinatorial structure of linked tableaux, which generalize the semi-standard tableaux that index a SAGBI basis of the Pl\"ucker coordinate ring of a flag variety. We show that linked tableaux index Domokos-Zubkov…
In our companion paper, we develop a new $SL_4$-web basis. Basis elements are given by certain planar graphs and are constructed so that important algebraic operations can be performed diagrammatically. A guiding principle behind our…
We introduce a new type of lattice path, called brick-wall lattice path, and we derive a formula which counts the number of paths on these lattices imposing certain restrictions on the Cartesian plane. Connections to the Fibonacci sequence,…
Young's lattice is a partial order on integer partitions whose saturated chains correspond to standard Young tableaux, one type of combinatorial object that generates the Schur basis for symmetric functions. Generalizing Young's lattice, we…
Let $\lambda$ be a partition, viewed as a Young diagram. We define the hook difference of a cell of $\lambda$ to be the difference of its leg and arm lengths. Define $h_{1,1}(\lambda)$ to be the number of cells of $\lambda$ with hook…
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;…
Set-valued tableaux formulas play an important role in Schubert calculus. Using the box greedy reduced word for the construction of the Macdonald polynomials, we convert the alcove walk formula for Macdonald polynomials to a set-valued…
In this paper, we introduce Jacobi polynomial generalizations of several classical invariants in coding theory over finite fields, specifically, the higher and extended weight enumerators, and we establish explicit correspondences between…
We describe recent work on preprojective algebras and moduli spaces of their representations. We give an analogue of Kac's Theorem, characterizing the dimension types of indecomposable coherent sheaves over weighted projective lines in…
We present a bijective proof of the hook-length formula for shifted standard tableaux of a fixed shape based on a modified jeu de taquin and the ideas of the bijective proof of the hook-length formula for ordinary standard tableaux by…
In this paper we introduce several quantitative methods for the lambda-calculus based on partial metrics, a well-studied variant of standard metric spaces that have been used to metrize non-Hausdorff topologies, like those arising from…
We give new product formulas for the number of standard Young tableaux of certain skew shapes and for the principal evaluation of the certain Schubert polynomials. These are proved by utilizing symmetries for evaluations of factorial Schur…
Recently, in papers by Knutson, Tao and Woodward, Henriques and Kamnitzer, Pak and Vallejo have been constructed several interesting bijections of associativity and commutativity. In the first two papers bijections relate special sets of…
We show that there are uncountably many countable lattices. We give a discussion of which such lattices can be modular or distributive. The method applies to show that certain other classes of structures also have uncountably many…
We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…