Kitaev, Sergey On multi-avoidance of right angled numbered polyomino patterns. (English) Zbl 1081.05024 Integers 4, Paper A21, 20 p. (2004). Summary: S. Kitaev, T. Mansour and A. Vella [On avoidance of numbered polyomino patterns; http://www.math.chalmers.se/Math/Research/Combinatorics/preprints/kitaev/kmv.ps] introduced numbered polyomino patterns that generalize the concept of pattern avoidance from permutations and words to numbered polyominoes. We study simultaneous avoidance of two or more right-angled numbered polyomino patterns, which are 0-1 labellings of the essentially unique convex two-dimensional polyomino shape with 3 tiles. It turns out that this study gives relations to several combinatorial structures. Cited in 1 Document MSC: 05B50 Polyominoes 05A15 Exact enumeration problems, generating functions Keywords:permutations; words PDFBibTeX XMLCite \textit{S. Kitaev}, Integers 4, Paper A21, 20 p. (2004; Zbl 1081.05024) Full Text: EuDML Online Encyclopedia of Integer Sequences: a(0) = 1, thereafter a(n) = 4n. Multiples of 10: a(n) = 10 * n. a(n) = 6*n + 4. a(n) = 10n+2. a(n) = 12*n + 4. a(n) = 3*2^n - 2. a(n) = 7 * 2^n - 6. Dimension of the space of weight 2n cusp forms for Gamma_0( 62 ). Number of 4 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (10;0) and (11;0). Number of 3 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (10;0) and (10;1). Number of 5 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) and (11;0). Number of 5 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01,1) and (11;0). Number of 3 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1) and (11;0). Number of 4 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1) and (11;0). Number of 3 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (10;0) and (01;1). Number of 4 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (10;0) and (01;1). Number of 2 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) and (01;1). Number of 3 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) and (01;1). Number of 4 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) and (01;1). The number of permutations avoiding simultaneously consecutive patterns 213 and 231.