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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Matrices without forbidden interval minors
 Surma, David ; Jelínek, Vít (advisor) ; Klazar, Martin (referee)
In the thesis, we study the structure of binary matrices which do not contain a pat- tern P as an interval minor. We also deal with matrices that are critical for P, i.e., matrices without P which after changing any 0-entry to 1-entry contain the forbidden pattern P. First, we describe matrices critical for any one-line pattern. Then we deal with all patterns with two rows and three columns which contain at most four 1-entries. Finally, we characterize the matrices critical for the alternating pattern of size 2 × 4. 1
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Hereditary classes of binary matrices
 Kučera, Stanislav ; Jelínek, Vít (advisor) ; Klazar, Martin (referee)
Interval minors of binary matrices were introduced by Jacob Fox in the study of Stanley-Wilf limits. We study what can be implied from their relation to the theory of pattern avoidance of submatrices, which is a very popular area of discrete mathematics. We start by characterizing matrices avoiding small interval minors. We then consider classes of matrices closed under interval minors and we find classes of matrices that cannot be described by a finite number of forbidden interval minors. We also define and study a variant of a classical extremal Tur'an- type question studied in the area of combinatorics of permutations and binary matrices and in combinatorial geometry. 1
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