The number of \(M\)-sequences and \(f\)-vectors
type: Item
instance of: scholarly article
title: The number of \(M\)-sequences and \(f\)-vectors
zbMATH Open document ID: 0928.05002
author: Svante Linusson
published in: Combinatorica
publication date: 1999-12-20T00:00:00Z
review text: The author gives a recursive formula for the number of \(M\)-sequences in terms of the number of variables and maximum degree. Given a multicomplex (i.e. a multiset system satisfying \(A \subset B \in {\mathcal M} \Rightarrow A \in {\mathcal M}\)) let \(m_i=| \{A \in {\mathcal M}: \deg A=i\}| \). The sequence \(m=(m_1,m_2,\dots)\) is the \(M\)-sequence of \({\mathcal M}\). It is shown that the numbers of \(M\)-sequences for at most 2 variables are powers of two and for at most 3 variables they are Bell numbers. An asymptotic estimate of the number of \(M\)-sequences is also given in the case when the number of variables is fixed. This estimate is used to show lower bounds for the number of polytopes with few vertices. A similar recursive formula is proven for the number of \(f\)-vectors of simplicial complexes.
reviewed by: András Pluhár
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 52B05
Mathematics Subject Classification ID: 05A16
zbMATH DE Number: 1381104
zbMATH Keywords: simplicial complexes
zbMATH Keywords: \(M\)-sequences
zbMATH Keywords: \(f\)-vectors
MaRDI profile type: Publication
full work available at URL: s004930050055
OpenAlex ID: W2069487012
DOI: 10.1007/S004930050055
description: scientific article; zbMATH DE number 1381104