Order shattering and Wilson's theorem

Katalin Friedl, Lajos Rónyai

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The notion of order shattering was introduced in Anstee et al. (Graphs Combin. 18 (2002) 59-73). Here, we pursue further the algebraic interpretation that was established there. With this tool we give a new proof and a generalization for Wilson's theorem on the diagonal form for the incidence matrices of t-subsets vs. k-subsets (European J. Combin. 11 (1990) 609-615). This allows a generalization of the corresponding rank formula modulo p, where p is an arbitrary prime.

Original languageEnglish
Pages (from-to)127-136
Number of pages10
JournalDiscrete Mathematics
Volume270
Issue number1-3
DOIs
Publication statusPublished - Aug 28 2003

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Keywords

  • Inclusion matrix
  • Shattered set
  • Wilson's rank formula

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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