John Shields

Corner descent and repeated inners in skew Schur compositions

We prove exact corner transport for marked skew Schur compositions under Hypotheses I–IV of McNamara and van Willigenburg, using Olson-Harris’s composition homomorphism. Generator-span separation identifies transported child functions with their multiplicities and reduces source-...

Skew computer-assisted composition necessity (forthcoming)

(Forthcoming)

Polynomial recognition and inflation of Hessenberg skew Schur classes

We recover the connected skew Schur class of every ribbon composite over a zero-free inner whose near-concatenation powers are rigid up to rotation. For three zero-free blocks with a rigid total merger, the connected class has one, two, or four members; commuting blocks admit leg...

Corner-cofactor descent for skew Schur compositions

We prove an exact formula for the extreme Jacobi–Trudi cofactor of a marked skew composition under Hypotheses I–IV of McNamara and van Willigenburg, without Hypothesis V, using Olson-Harris's composition homomorphism. The formula separates the compositions of the outer diagram's...

Skew computer-assisted composition necessity (forthcoming)

(Forthcoming)

Corner-cofactor descent for skew Schur compositions

We prove an exact formula for the extreme Jacobi–Trudi cofactor of a marked skew composition under Hypotheses I–IV of McNamara and van Willigenburg, without Hypothesis V, using Olson-Harris's composition homomorphism. The formula separates the compositions of the outer diagram's...

Skew Schur equivalence by Jacobi–Trudi negative count

We classify connected skew diagrams with at most six negative indices in their full row Jacobi–Trudi board, against arbitrary skew diagrams with the same Schur function. Seven parameter families give all exceptional classes, each with four members; every other source is determine...

Class recovery and inflation for repeated-block skew diagrams

We recover complete connected skew Schur classes for two specified repeated-block constructions. For separated constant-gap inners repeated at least twice, every mate comes from the outer ribbon class and global rotation, without assuming that the inner diagram is rigid. Symmetri...

Local common-factor gluing for skew Schur functions

We prove that every component of the common-factor graph of a skew Schur class is a clique. Each rooted component is the fiber of any source-minimal chart at any of its vertices. Edges encode proper marked compositions with a common final factor and Schur-equal outer factors, und...

Local common-factor gluing for skew Schur functions

We prove that every component of the common-factor graph of a skew Schur class is a clique. Each rooted component is the fiber of any source-minimal chart at any of its vertices. Edges encode proper marked compositions with a common final factor and Schur-equal outer factors, und...

Polynomial recognition and inflation of Hessenberg skew Schur classes

We recover the connected skew Schur class of every ribbon composite over a zero-free inner whose near-concatenation powers are rigid up to rotation. For three zero-free blocks with a rigid total merger, the connected class has one, two, or four members; commuting blocks admit leg...

Power rigidity and inflation for constant-excess skew diagrams

We classify all connected skew Schur mates of repeated constant-excess diagrams under profile inflation when the inner gap word has unequal endpoints, is symmetric, or satisfies a specified balanced-prefix condition. These domains include every constant-excess inner with at most...

Cofactor independence and dilation for skew Schur functions

The signed cofactors of a Jacobi–Trudi matrix with strictly positive indices are linearly independent over the rationals unless its skew diagram is fixed by rotation. In the symmetric case, reflection gives every relation and an explicit independent half of the cofactors. We prov...

Cofactor independence and dilation for skew Schur functions

The signed cofactors of a Jacobi–Trudi matrix with strictly positive indices are linearly independent over the rationals unless its skew diagram is fixed by rotation. In the symmetric case, reflection gives every relation and an explicit independent half of the cofactors. We prov...