scholarly journals Combinatorial Construction of Locally Testable Codes

2009 ◽  
Vol 39 (2) ◽  
pp. 491-544 ◽  
Author(s):  
Or Meir
2000 ◽  
Vol 3 ◽  
pp. 96-116 ◽  
Author(s):  
Catherine Greenhill

AbstractThe exterior square of a multiset is a natural combinatorial construction which is related to the exterior square of a vector space. We consider multisets of elements of an abelian group. Two properties are defined which a multiset may satisfy: recognisability and involution-recognisability. A polynomial-time algorithm is described which takes an input multiset and returns either (a) a multiset which is either recognisable or involution-recognisable and whose exterior square equals the input multiset, or (b) the message that no such multiset exists. The proportion of multisets which are neither recognisable nor involution-recognisable is shown to be small when the abelian group is finite but large. Some further comments are made about the motivating case of multisets of eigenvalues of matrices.


10.37236/1263 ◽  
1995 ◽  
Vol 3 (2) ◽  
Author(s):  
Donald E. Knuth

A combinatorial construction proves an identity for the product of the Pfaffian of a skew-symmetric matrix by the Pfaffian of one of its submatrices. Several applications of this identity are followed by a brief history of Pfaffians.


2017 ◽  
Vol 64 (2) ◽  
pp. 1-42 ◽  
Author(s):  
Swastik Kopparty ◽  
Or Meir ◽  
Noga Ron-Zewi ◽  
Shubhangi Saraf

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