Browsing by Author "Mansour, T."
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Item Open Access An algorithmic approach based on generating trees for enumerating pattern-avoiding inversion sequences(Academic Press Ltd- Elsevier Science Ltd, 2023-05-18) Kotsireas, I.; Mansour, T.; Yıldırım, GökhanWe introduce an algorithmic approach based on a generating tree method for enumerating the inversion sequences with various pattern-avoidance restrictions. For a given set of patterns, we propose an algorithm that outputs either an accurate description of the succession rules of the corresponding generating tree or an ansatz. By using this approach, we determine the generating trees for the pattern classes In(000, 021), In(100, 021), In(110, 021), In(102, 021), In(100, 012), In(011, 201), In(011, 210) and In(120, 210). Then we use the kernel method, obtain generating functions of each class, and find enumerating formulas. Lin and Yan studied the classification of the Wilf-equivalences for inversion sequences avoiding pairs of length-three patterns and showed that there are 48 Wilf classes among 78 pairs. In this paper, we solve six open cases for such pattern classes. Moreover, we extend the algorithm to restricted growth sequences and apply it to several classes. In particular, we present explicit formulas for the generating functions of the restricted growth sequences that avoid either {12313, 12323}, {12313, 12323, 12333}, or {123 ··· 1}.Item Open Access A decomposition of column-convex polyominoes and two vertex statistics(Springer, 2022-04-27) Cakić, N.; Mansour, T.; Yıldırım, GökhanWe introduce a decomposition method for column-convex polyominoes and enumerate them in terms of two statistics: the number of internal vertices and the number of corners in the boundary. We first find the generating function for the column-convex polyominoes according to the horizontal and vertical half-perimeter, and the number of interior vertices. In particular, we show that the average number of interior vertices over all column-convex polyominoes of perimeter 2n is asymptotic to αon3 / 2 where αo≈ 0.57895563 …. We also find the generating function for the column-convex polyominoes according to the horizontal and vertical half-perimeter, and the number of corners in the boundary. In particular, we show that the average number of corners over all column-convex polyominoes of perimeter 2n is asymptotic to α1n where α1≈ 1.17157287 …. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.Item Open Access Enumerations of bargraphs with respect to corner statistics(University of Belgrade, 2020) Mansour, T.; Yıldırım, GökhanWe study the enumeration of bargraphs with respect to some corner statistics. We find generating functions for the number of bargraphs that track the corner statistics of interest, the number of cells, and the number of columns. We also consider bargraph representation of set partitions and obtain some explicit formulas for the number of specific types of corners in such representations.Item Open Access Longest increasing subsequences in involutions avoiding patterns of length three(TÜBİTAK, 2019-07) Mansour, T.; Yıldırım, GökhanWe study the longest increasing subsequences in random involutions that avoid the patterns of length three under the uniform probability distribution. We determine the exact and asymptotic formulas for the average length of the longest increasing subsequences for such permutation classes.Item Open Access Permutations avoiding 312 and another pattern, Chebyshev polynomials and longest increasing subsequences(Elsevier, 2020) Mansour, T.; Yıldırım, GökhanWe study the longest increasing subsequence problem for random permutations avoiding the pattern 312 and another pattern τ under the uniform probability distribution. We determine the exact and asymptotic formulas for the average length of the longest increasing subsequences for such permutation classes specifically when the pattern τ is monotone increasing or decreasing, or any pattern of length four.