“School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

Paper   IPM / M / 8742
School of Mathematics
  Title:   Inclusion matrices and chains
  Author(s): 
1.  E. Ghorbani
2.  G. B. Khosrovshahi
3.  Ch. Maysoori
4.  M. Mohammad-Noori
  Status:   Published
  Journal: J. Combin. Theory Ser. A
  Vol.:  115
  Year:  2008
  Pages:   878-887
  Supported by:  IPM
  Abstract:
Given integers t, k, and v such that 0 ≤ tkv, let Wtk(v) be the inclusion matrix of t-subsets vs. k-subsets of a v-set. We modify slightly the concept of standard tableau to study the notion of rank of a finite set of positive integers which was introduced by Frankl. Utilizing this, a decomposition of the poset 2[v] into symmetric skipless chains is given. Based on this decomposition, we construct an inclusion matrix, denoted by Wtk(v), which is row-equivalent to Wtk(v). Its Smith normal form is determined. As applications, Wilson's diagonal form of Wtk(v) is obtained as well as a new proof of the well known theorem on the necessary and sufficient conditions for existence of integral solutions of the system Wtkx=b due to Wilson. Finally we present anotherinclusion matrix with similar properties to those of Wtk(v) which is in some way equivalent to Wtk(v).

Download TeX format
back to top
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
scroll left or right