Year: 2025
Type: article
Abstract: Segre products of posets were defined by Björner and Welker (2005).We investigate the homology representations of the t-fold Segre power B (t) n of the Boolean lattice B n .The direct product S ×t n of the symmetric group S n acts on the homology of rank-selected subposets of B (t) n .We give an explicit formula for the decomposition into S ×t n -irreducibles of the homology of the full poset, as well as formulas for the diagonal action of the symmetric group S n .For the rank-selected homology, we show that the stable principal specialisation of the product Frobenius characteristic of the S ×t n -module coincides with the corresponding rank-selected invariant of the t-fold Segre power of the subspace lattice.
Authors: Yifei Li, Sheila Sundaram
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4410048777