Quotient sets and subset-subspace analogy
type: Item
instance of: scholarly article
title: Quotient sets and subset-subspace analogy
zbMATH Open document ID: 0937.05003
author: Jun Wang
published in: Advances in Applied Mathematics
publication date: 2000-06-04T00:00:00Z
review text: Using Knuth's fundamental observation about the rank and order preserving map from the lattice of the finite linear subspace lattice \({\mathcal L}_q(n)\) to the Boolean lattice \(B_n,\) this paper exhibits an isomorphism between the Boolean lattice \(B_n\) and the quotient lattice \({\mathcal L}_q(n) / T_n(q),\) where \(T_n(q)\) is the subgroup of the general linear group \(\text{GL}_n(q)\) consisting of all upper triangular matrices. This structure theorem gives combinatorial interpretations of taking the limit \(q \rightarrow 1\) in certain \(q\)-identities.
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A30
zbMATH DE Number: 1394761
zbMATH Keywords: Boolean lattice
zbMATH Keywords: subspace lattice
zbMATH Keywords: structure theorem
reviewed by: Péter L. Erdős
MaRDI profile type: Publication
full work available at URL: aama.1999.0654
OpenAlex ID: W1980825014
cites work: On the Foundations of Combinatorial Theory IV Finite Vector Spaces and Eulerian Generating Functions
cites work: \(q\)-analogs of the inclusion-exclusion principle and permutations with restricted position
cites work: Subspaces, subsets, and partitions
cites work: Mappings of subspaces into subsets
cites work: A combinatorial interpretation of q-derangement and q-Laguerre numbers
cites work: Q3748279
DOI: 10.1006/AAMA.1999.0654
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description: scientific article; zbMATH DE number 1394761