# Order shattering and Wilson's theorem

Katalin Friedl, L. 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 language English 127-136 10 Discrete Mathematics 270 1-3 https://doi.org/10.1016/S0012-365X(02)00869-5 Published - Aug 28 2003

### Fingerprint

Wilson's theorem
Incidence Matrix
Subset
Modulo
Arbitrary
Graph in graph theory
Generalization

### Keywords

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

### ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics
• Theoretical Computer Science

### Cite this

Order shattering and Wilson's theorem. / Friedl, Katalin; Rónyai, L.

In: Discrete Mathematics, Vol. 270, No. 1-3, 28.08.2003, p. 127-136.

Research output: Contribution to journalArticle

Friedl, Katalin ; Rónyai, L. / Order shattering and Wilson's theorem. In: Discrete Mathematics. 2003 ; Vol. 270, No. 1-3. pp. 127-136.
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