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The Alpha Function of a Matroid—I. Transversal Matroids
Author(s) -
Kung Joseph. P. S.
Publication year - 1978
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1978583263
Subject(s) - matroid , transversal (combinatorics) , mathematics , combinatorics , function (biology) , alpha (finance) , recursion (computer science) , discrete mathematics , mathematical analysis , algorithm , construct validity , statistics , evolutionary biology , biology , psychometrics
Let n be the nullity function of the matroid G ( S ). The Mason alpha function is defined on subsets A of S by the recursion α( A )= n ( A )−∑ F⊂A α( F ), the summation being over all flats F strictly contained in A . The alpha function may be viewed as the first difference of the nullity. We study the behavior of a under strong maps, and apply our results to proving Mason's alpha criterion: a matroid is the dual of a transversal matroid if and only if its alpha function is non‐negative.