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 |
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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 journal › Article
}
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 -