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. Symmetric inners remove the otherwise separate orientation copy. For an asymmetric two-row inner, adding the same nonnegative integer to every row length and adjacent overlap-minus-one preserves the full class below the shorter row's excess over the inner gap. At that exact threshold, and at every larger inflation, only rotation remains. Inflation is injective: the images of formerly equal diagrams split into distinct classes. Total contraction proves the first inverse; a lowest-degree boundary determinant with private column residues proves the second. Both theorems quantify over arbitrary connected mates.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-04
DOI
https://doi.org/10.5281/zenodo.23133728
Primary Topic
Advanced Combinatorial Mathematics
Type
preprint
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preprint

Class recovery and inflation for repeated-block skew diagrams

John Shields
Zenodo (CERN European Organization for Nuclear Research)
Advanced Combinatorial Mathematics
preprint

Class recovery and inflation for repeated-block skew diagrams

John Shields
preprint en

Abstract

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. Symmetric inners remove the otherwise separate orientation copy. For an asymmetric two-row inner, adding the same nonnegative integer to every row length and adjacent overlap-minus-one preserves the full class below the shorter row's excess over the inner gap. At that exact threshold, and at every larger inflation, only rotation remains. Inflation is injective: the images of formerly equal diagrams split into distinct classes. Total contraction proves the first inverse; a lowest-degree boundary determinant with private column residues proves the second. Both theorems quantify over arbitrary connected mates.

Zenodo (CERN European Organization for Nuclear Research)
Advanced Combinatorial Mathematics
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