Related papers: A composition method for neat formulas of chromati…
We introduce a new combinatorial object, semistandard increasing decomposition tableau and study its relation to a semistandard decomposition tableau introduced by Kra\'skiewicz and developed by Lam and Serrano. We also introduce…
In this article, we will prove the Giambelli formula for Schur multiple zeta-functions of extended shape which we call laced type, using the combinatorial method of proving the Giambelli formula for Schur function by Egecioglu and Remmel.…
Protocols do not work alone, but together, one protocol relying on another to provide needed services. Many of the problems in cryptographic protocols arise when such composition is done incorrectly or is not well understood. In this paper…
The characters of Kazhdan--Lusztig elements of the Hecke algebra over $S_n$ (and in particular, the chromatic symmetric function of indifference graphs) are completely encoded in the (intersection) cohomology of certain subvarieties of the…
The Compositional Integral is defined, formally constructed, and discussed. A direct generalization of Riemann's construction of the integral; it is intended as an alternative way of looking at First Order Differential Equations. This brief…
Cylindric Schur functions are a family of symmetric functions that generalize skew Schur functions. We give a short proof that skew cylindric Schur functions expand positively in terms of non-skew cylindric Schur functions. In particular,…
We study the class $\mathcal C$ of symmetric functions whose coefficients in the Schur basis can be described by generating functions for sets of tableaux with fixed shape. Included in this class are the Hall-Littlewood polynomials,…
We present a method to compute the class expansion of a symmetric function in the Jucys-Murphy elements of the symmetric group. We apply this method to one-row Hall-Littlewood symmetric functions, which interpolate between power sums and…
Crew and Spirklt generalize Stanley's chromatic symmetric function to vertex-weighted graphs. One of the primary motivations for extending the chromatic symmetric function to vertex-weighted graphs is the existence of a deletion-contraction…
We consider interpolation of univariate functions on arbitrary sets of nodes by Gaussian radial basis functions or by exponential functions. We derive closed-form expressions for the interpolation error based on the…
The paper studies complementary choice functions, i.e. monotonic and consistent choice functions. Such choice functions were introduced and used in the work \cite{RY} for investigation of matchings with complementary contracts. Three…
We give a Littlewood-Richardson type rule for expanding the product of a row-strict quasisymmetric Schur function and a symmetric Schur function in terms of row-strict quasisymmetric Schur functions. This expansion follows from several new…
For $a,b\in\mathbb{N}_0$, we consider $(an+b)$-color compositions of a positive integer $\nu$ for which each part of size $n$ admits $an+b$ colors. We study these compositions from the enumerative point of view and give a formula for the…
The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.
We define a new type of vertex coloring which generalizes vertex coloring in graphs, hypergraphs, and simplicial complexes. This coloring also generalizes oriented coloring, acyclic coloring, and star coloring. There is an associated…
The involution Stanley symmetric functions $\hat{F}_y$ are the stable limits of the analogues of Schubert polynomials for the orbits of the orthogonal group in the flag variety. These symmetric functions are also generating functions for…
Ternary logic is expected to increase the area efficiency of VLSI due to its expressiveness compared to the traditional binary logic. This paper proposes a new symmetric ternary logic and a systematic logic composition methodology that…
This paper realizes of two families of combinatorial symmetric functions via the complex character theory of the finite general linear group $\mathrm{GL}_{n}(\mathbb{F}_{q})$: chromatic quasisymmetric functions and vertical strip LLT…
Let $\mathfrak g$ be a Borcherds algebra with the associated graph $G$. We prove that the chromatic symmetric function of $G$ can be recovered from the Weyl denominator identity of $\mathfrak g$ and this gives a Lie theoretic proof of…
Egge, Loehr, and Warrington proved a formula for the Schur function expansion of a symmetric function in terms of its expansion in fundamental quasi-symmetric functions. Their formula involves the coefficients of a modified inverse Kostka…