The normalized matching property from the generalized Macaulay theorem

Order ◽  
1995 ◽  
Vol 12 (3) ◽  
pp. 233-237
Author(s):  
G. F. Clements
Keyword(s):  
Normalized Matching Property

scholarly journals NORMALIZED MATCHING PROPERTY OF A CLASS OF SUBSPACE LATTICES

2007 ◽  
Vol 11 (1) ◽  
pp. 43-50 ◽  
Author(s):  
Jun Wang ◽  
Huajun Zhang
Keyword(s):  
Normalized Matching Property ◽  
Subspace Lattices

scholarly journals A Finite Word Poset

10.37236/1607 ◽  
2000 ◽  
Vol 8 (2) ◽  
Author(s):  
Péter L. Erdős ◽  
Péter Sziklai ◽  
David C. Torney
Keyword(s):  
Automorphism Groups ◽  
Partial Ordering ◽  
Finite Alphabet ◽  
Combinatorial Properties ◽  
Normalized Matching Property ◽  
Finite Word

Our word posets have finite words of bounded length as their elements, with the words composed from a finite alphabet. Their partial ordering follows from the inclusion of a word as a subsequence of another word. The elemental combinatorial properties of such posets are established. Their automorphism groups are determined (along with similar result for the word poset studied by Burosch, Frank and Röhl [4]) and a BLYM inequality is verified (via the normalized matching property).

Normalized Matching Property of Restricted Subspace Lattices

2008 ◽  
Vol 22 (1) ◽  
pp. 248-255 ◽  
Author(s):  
Jun Wang ◽  
Huajun Zhang
Keyword(s):  
Normalized Matching Property ◽  
Subspace Lattices

scholarly journals The Normalized Matching Property in Random and Pseudorandom Bipartite Graphs

10.37236/9148 ◽  
2021 ◽  
Vol 28 (2) ◽  
Author(s):  
Niranjan Balachandran ◽  
Deepanshu Kush
Keyword(s):  
Bipartite Graph ◽  
Perfect Matching ◽  
Decomposition Theorem ◽  
Discrete Math ◽  
Bipartite Graphs ◽  
Classic Result ◽  
Normalized Matching Property ◽  
Vertex Partition ◽  
Vertex Set

A bipartite graph $G(X,Y,E)$ with vertex partition $(X,Y)$ is said to have the Normalized Matching Property (NMP) if for any subset $S\subseteq X$ we have $\frac{|N(S)|}{|Y|}\geq\frac{|S|}{|X|}$. In this paper, we prove the following results about the Normalized Matching Property.  The random bipartite graph $\mathbb{G}(k,n,p)$ with $|X|=k,|Y|=n$, and $k\leq n<\exp(k)$, and each pair $(x,y)\in X\times Y$ being an edge in $\mathbb{G}$ independently with probability $p$ has $p=\frac{\log n}{k}$ as the threshold for NMP. This generalizes a classic result of Erdős-Rényi on the $\frac{\log n}{n}$ threshold for the existence of a perfect matching in $\mathbb{G}(n,n,p)$. A bipartite graph $G(X,Y)$, with $k=|X|\le |Y|=n$, is said to be Thomason pseudorandom (following A. Thomason (Discrete Math., 1989)) with parameters $(p,\varepsilon)$ if every $x\in X$ has degree at least $pn$ and every pair of distinct $x, x'\in X$ have at most $(1+\varepsilon)p^2n$ common neighbours. We show that Thomason pseudorandom graphs have the following property: Given $\varepsilon>0$ and $n\geq k\gg 0$, there exist functions $f,g$ with $f(x), g(x)\to 0$ as $x\to 0$, and sets $\mathrm{Del}_X\subset X, \  \mathrm{Del}_Y\subset Y$ with $|\mathrm{Del}_X|\leq f(\varepsilon)k,\ |\mathrm{Del}_Y|\leq g(\varepsilon)n$ such that $G(X\setminus \mathrm{Del}_X,Y\setminus \mathrm{Del}_Y)$ has NMP. Enroute, we prove an 'almost' vertex decomposition theorem: Every Thomason pseudorandom bipartite graph $G(X,Y)$ admits - except for a negligible portion of its vertex set - a partition of its vertex set into graphs that are spanned by trees that have NMP, and which arise organically through the Euclidean GCD algorithm. 

Normalized Matching Property of Posets Generated by Orbits of Subspaces Under Finite Symplectic Groups

2013 ◽  
Vol 42 (4) ◽  
pp. 1711-1717 ◽  
Author(s):  
Jun Guo ◽  
Fenggao Li ◽  
Kaishun Wang
Keyword(s):  
Symplectic Groups ◽  
Normalized Matching Property ◽  
Finite Symplectic Groups

scholarly journals Normalized matching property of the subgroup lattice of an abelian p-group

2002 ◽  
Vol 257 (2-3) ◽  
pp. 559-574 ◽  
Author(s):  
Jun Wang
Keyword(s):  
Subgroup Lattice ◽  
Normalized Matching Property

scholarly journals Normalized matching property of subspace posets in finite classical polar spaces

2013 ◽  
Vol 19 (1) ◽  
pp. 67-72 ◽  
Author(s):  
Jun Guo ◽  
Kaishun Wang ◽  
Fenggao Li
Keyword(s):  
Polar Spaces ◽  
Normalized Matching Property ◽  
Classical Polar Spaces
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