Differential posets have strict rank growth: a conjecture of Stanley
Alexander Miller
TL;DR
This paper proves that the rank function of an r-differential poset grows strictly, using advanced representation theoretic techniques to confirm a conjecture by Stanley.
Contribution
It establishes the strict growth of the rank function in r-differential posets, confirming Stanley's conjecture through novel application of representation theory.
Findings
Confirmed strict rank growth in r-differential posets
Applied representation theoretic techniques to poset growth
Validated Stanley's conjecture on differential posets
Abstract
We establish strict growth for the rank function of an r-differential poset. We do so by exploiting the representation theoretic techniques developed by Reiner and the author for studying related Smith forms.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry