### 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 |
---|---|

Pages (from-to) | 127-136 |

Number of pages | 10 |

Journal | Discrete Mathematics |

Volume | 270 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Aug 28 2003 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*270*(1-3), 127-136. https://doi.org/10.1016/S0012-365X(02)00869-5

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

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 270, no. 1-3, pp. 127-136. https://doi.org/10.1016/S0012-365X(02)00869-5

}

TY - JOUR

T1 - Order shattering and Wilson's theorem

AU - Friedl, Katalin

AU - Rónyai, L.

PY - 2003/8/28

Y1 - 2003/8/28

N2 - 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.

AB - 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.

KW - Inclusion matrix

KW - Shattered set

KW - Wilson's rank formula

UR - http://www.scopus.com/inward/record.url?scp=0042531875&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042531875&partnerID=8YFLogxK

U2 - 10.1016/S0012-365X(02)00869-5

DO - 10.1016/S0012-365X(02)00869-5

M3 - Article

AN - SCOPUS:0042531875

VL - 270

SP - 127

EP - 136

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -