Young bitableaux, lattice paths and Hilbert functions

DOI10.1016/0378-3758(95)00156-5zbMath0864.05088OpenAlexW2043873939MaRDI QIDQ1923405

Sudhir R. Ghorpade

Publication date: 9 June 1997

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0378-3758(95)00156-5

zbMATH Keywords

determinantal idealsStanley-Reisner ringnonintersecting lattice pathsSchubert varietiesHilbert functionHilbert polynomialHilbert seriesstraightening lawstandard bitableauxAbhyankar formula

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial aspects of representation theory (05E10) Linkage, complete intersections and determinantal ideals (13C40) Determinantal varieties (14M12) Grassmannians, Schubert varieties, flag manifolds (14M15) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40)

Related Items (3)

Mixed Hilbert coefficients of homogeneous \(d\)-sequences and quadratic sequences ⋮ Computation of the a-invariant of ladder determinantal rings ⋮ Hilbert functions of points on Schubert varieties in the symplectic Grassmannian

Cites Work

• Enumeration of higher-dimensional paths under restrictions
• Binomial determinants, paths, and hook length formulae
• Über Streckungsringe. (On rings with straightening law)
• Young tableaux and linear independence of standard monomials in multiminors of a multimatrix
• Combinatorial meaning of the coefficients of a Hilbert polynomial
• Gröbner bases and multiplicity of determinantal and Pfaffian ideals
• On the computation of a-invariants
• Bijection between indexed monomials and standard bitableaux
• Counting nonintersecting lattice paths with turns
• Young multitableaux and higher dimensional determinants
• On the Foundations of Combinatorial Theory: IX Combinatorial Methods in Invariant Theory
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