✦ LIBER ✦

A short proof of a conjecture on quasi-symmetric 3-designs

✍ Scribed by Rajendra M. Pawale; Sharad S. Sane

Publisher: Elsevier Science
Year: 1991
Tongue: English
Weight: 150 KB
Volume: 96
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90472-e

No coin nor oath required. For personal study only.

✦ Synopsis

Pawale, R.M. and S.S. Sane, A short p,oof of a conjecture on quasi-symmetric 2-designs, Discrete Mathematics 96 (1991) 71-74.

It was conjettured by Sane and M.S. Shrikhande that the only nontrivial quasi-symmetric 3-design with the smaller block intersection number one is either the Witt 4-(23, 7, 1) design or its residual. Calderbank and Morton recently proved this conjecture using sophisticated number theoretic arguments. A short and elementary proof of this conjecture is presented in this paper.

📜 SIMILAR VOLUMES

On a conjecture of jungnickel and tonche

On a conjecture of jungnickel and tonchev for quasi-symmetric designs

✍ Yury J. Ionin; Mohan S. Shrikhande 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 582 KB

Jungnickel and Tonchev conjectured in [4] that if a quasi-symmetric design D is an s-fold quasi-multiple of a symmetric (v,k, A) design with (k, (sl)A) = 1, then D is a multiple. We prove this conjecture under any one of the conditions: s 5 7, k -1 is prime, or the design D is a 3-design. It is show

A note on triangle-free quasi-symmetric

A note on triangle-free quasi-symmetric designs

✍ Rajendra M. Pawale 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 84 KB 👁 1 views

Triangle-free quasi-symmetric 2-(v, k,k) designs with intersection numbers x, y; 01, are investigated. It is proved that k ≥ 2 yx -3. As a consequence it is seen that for fixed k, there are finitely many triangle-free quasi-symmetric designs. It is also proved that: k ≤ y( yx)+ x.

A short proof of a theorem of dirac's ab

A short proof of a theorem of dirac's about hadwiger's conjecture

✍ D. R. Woodall 📂 Article 📅 1992 🏛 John Wiley and Sons 🌐 English ⚖ 105 KB 👁 1 views

## Abstract A Short proof is given of the theorem that every grph that does not have __K__~4~ as a subcontraction is properly vertex 3‐colorable.

A short proof of a ‘strange’ combinatori

A short proof of a ‘strange’ combinatorial identity conjectured by Gosper

✍ Shalosh B. Ekhad 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 75 KB

Ekhad, S.B., A short proof of a 'strange' combinatorial identity conjectured by Gosper, Discrete Mathematics 90 (1991) 319-320.

Proof of a conjecture on game domination

✍ O. Favaron; H. Karami; R. Khoeilar; S. M. Sheikholeslami; L. Volkmann 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 87 KB 👁 1 views

## Abstract The game domination number of a (simple, undirected) graph is defined by the following game. Two players, \documentclass{article}\usepackage{amssymb}\usepackage{amsbsy}\usepackage[mathscr]{euscript}\footskip=0pc\pagestyle{empty}\begin{document}${\mathcal{A}}$\end{document} and \docume

Proof of a conjecture on Genocchi number

Proof of a conjecture on Genocchi numbers

✍ John Riordan; Paul R. Stein 📂 Article 📅 1973 🏛 Elsevier Science 🌐 English ⚖ 446 KB

In [ I ]I, Gandhi has stated the following conjecture on Genocchi numbl:rs: ## . z;(t~-I)~ . The meaning of the odd notation on the 1e:ft of (1) is as follows: write . . . C(k+n-1)2 ; then ## K(n+l,k)=k2K(n,k+lj-(k-l)2~(~~,k~ K(1,k)=k2-(k-1;j2 =2k--1 alId, af course, (1) is restated as (1')