Flagged Hamel--Goulden formulas

2025/12/15 by Alibek Adilzhan, Damir Yeliussizov, Adilzhan, Alibek +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2512.13265

Abstract

We obtain Hamel--Goulden-type ribbon decomposition determinantal formulas for flagged supersymmetric Schur functions. As an application, we derive corresponding new determinantal formulas dual refined canonical stable Grothendieck polynomials. These results generalize and produce a number of new determinantal formulas for these symmetric functions including Jacobi--Trudi and skew Giambelli-type determinants.

Citations

• Refined canonical stable Grothendieck polynomials and their duals, Part 2
• Free-fermions and canonical Grothendieck polynomials
• Refined canonical stable Grothendieck polynomials and their duals, Part 1
• Bijecting hidden symmetries for skew staircase shapes
• The Stembridge Equality for Skew Stable Grothendieck Polynomials and Skew Dual Stable Grothendieck Polynomials
• Refined dual Grothendieck polynomials, integrability, and the Schur measure
• Jacobi--Trudi formulas for flagged refined dual stable Grothendieck polynomials
• Determinantal formulas for dual Grothendieck polynomials
• Jacobi--Trudi formula for refined dual stable Grothendieck polynomials
• Dual Grothendieck polynomials via last-passage percolation
• Enumeration of plane partitions by descents
• Random plane partitions and corner distributions
• Combinatorial Hopf algebras and K-homology of Grassmanians
• Transformations of Border Strips and Schur Function Determinants

Related

• Transformations of Border Strips and Schur Function Determinants
• Factorial supersymmetric skew Schur functions and ninth variation determinantal identities
• Flagged Grothendieck polynomials
• Determinantal formulas for dual Grothendieck polynomials
• Factorial Flagged Grothendieck Polynomials