The Genomic Schur Function is Fundamental-Positive

The Flagged Double Schur Function

The double Schur function is a natural generalization of the factorial Schur function introduced by Biedenharn and Louck. It also arises as the symmetric double Schubert polynomial corresponding to a class of permutations called Grassmannian permutations introduced by A. Lascoux. We present a lattice path interpretation of the double Schur function based on a flagged determinantal definition, w...

Schur-convexity, Schur-geometric and Schur-harmonic convexity for a composite function of complete symmetric function

In this paper, using the properties of Schur-convex function, Schur-geometrically convex function and Schur-harmonically convex function, we provide much simpler proofs of the Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity for a composite function of the complete symmetric function.

Staircase Skew Schur Functions Are Schur P -positive

We prove Stanley’s conjecture that, if δn is the staircase shape, then the skew Schur functions sδn/μ are non-negative sums of Schur P -functions. We prove that the coefficients in this sum count certain fillings of shifted shapes. In particular, for the skew Schur function sδn/δn−2 , we discuss connections with Eulerian numbers and alternating permutations.

A Schur Function Identity

SOLVING FUZZY LINEAR SYSTEMS BY USING THE SCHUR COMPLEMENT WHEN COEFFICIENT MATRIX IS AN M-MATRIX

This paper analyzes a linear system of equations when the righthandside is a fuzzy vector and the coefficient matrix is a crisp M-matrix. Thefuzzy linear system (FLS) is converted to the equivalent crisp system withcoefficient matrix of dimension 2n × 2n. However, solving this crisp system isdifficult for large n because of dimensionality problems . It is shown that thisdifficulty may be avoide...