Displaying similar documents to “On multi-avoidance of right angled numbered polyomino patterns.”

The box parameter for words and permutations

Helmut Prodinger (2014)

Open Mathematics

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The box parameter for words counts how often two letters w j and w k define a “box” such that all the letters w j+1; ..., w k−1 fall into that box. It is related to the visibility parameter and other parameters on words. Three models are considered: Words over a finite alphabet, permutations, and words with letters following a geometric distribution. A typical result is: The average box parameter for words over an M letter alphabet is asymptotically given by 2n − 2n H M/M, for fixed...

A note on preserving the spark of a matrix

Marcin Skrzyński (2015)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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Let Mm×n(F) be the vector space of all m×n matrices over a field F. In the case where m ≥ n, char(F) ≠ 2 and F has at least five elements, we give a complete characterization of linear maps Φ: Mm×n(F) → Mm×n(F) such that spark(Φ(A)) = spark(A) for any A ∈Mm×n(F).

Basic Properties of Determinants of Square Matrices over a Field 1

Karol Pąk (2007)

Formalized Mathematics

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In this paper I present basic properties of the determinant of square matrices over a field and selected properties of the sign of a permutation. First, I define the sign of a permutation by the requirement [...] where p is any fixed permutation of a set with n elements. I prove that the sign of a product of two permutations is the same as the product of their signs and show the relation between signs and parity of permutations. Then I consider the determinant of a linear combination...