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References [1] Ptaszynski M., Masui F., Rzepka R., Araki K., First Glance on Pattern-based Language Modeling , Language Acquisition and Understanding Research Group Technical Reports, 2014. [2] Ptaszynski M., Masui F., Kimura Y., Rzepka R., Araki K., Extracting Patterns of Harmful Expressions for Cyberbullying Detection , Proceedings of LTC’15, 2016, 370-375. [3] Ptaszynski M., Masui F., Rzepka R., Araki K., Subjective? Emotional? Emotive?: Language Combinatorics based Automatic Detection of Emotionally Loaded Sentences , Linguistics and Literature Studies

Mathematics of Chessboard Problems, Princeton University Press, 2004. [6] Zhao, K. The Combinatorics of Chessboards, Ph.D. dissertation, City University of New York, 1998.

References [1] A. Bacher, O. Bodini and A. Jacquot, Efficient random sampling of binary and unarybinary trees via holonomic equations, at [2] A. Bacher, O. Bodini and A. Jacquot, Exact-size sampling for Motzkin trees in linear time via Boltzmann samplers and holonomic specification, in: M. Nebel and W. Szpankowski (Eds.), Prooceedings of the 10th Workshop on Analytic Algorithmics and Combinatorics (ANALCO), SIAM Press ed., (2013) 52-61. [3] F. Bassino and C. Nicaud, Enumeration and random generation of accessible automata, Theoret

+ k Queens Problem”, College Mathematics Journal , 40(3), 204–210, 2009. [6] Chatham, R.D., Doyle, M., Jeffers, R.J., Kosters, W.A., Skaggs, R.D., Ward, J.A. “Centrosymmetric solutions to chessboard separation problems”, Bulletin of the Institute of Combinatorics and its Applications , 65, 6–26, 2012. [7] Kaplansky, I. “Symbolic solution of certain problems in permutations”, Bulletin of the American Mathematical Society 50, 906–914, 1944. [8] Sloane, N.J.A. Sequence A002464 in The On-Line Encyclopedia of Integer Sequences , 2017.

] PHILIPP, W.: Limit theorems for lacunary series and uniform distribution mod 1. Acta Arith. 26 (1974/75), no. 3, 241-251. [14] SHKREDOV, I. D.: Some new results on higher energies. Trans. Moscow Math. Soc. 74 (2013), 31-63. [15] TAO, T.-VU. V.: Additive Combinatorics. Cambridge University Press, Cambridge U.K., 2006.


We investigate a type of a Sudoku variant called Sudo-Kurve, which allows bent rows and columns, and develop a new, yet equivalent, variant we call a Sudo-Cube. We examine the total number of distinct solution grids for this type with or without symmetry. We study other mathematical aspects of this puzzle along with the minimum number of clues needed and the number of ways to place individual symbols.

), 3155-3173. [4] M. Dodig, M. Stošić, Combinatorics of column minimal indices and matrix pencil completion problems, SIAM J. Matrix Anal. Appl., 31 (2010), 2318-2346. [5] M. Dodig, M. Stošić, On convexity of polynomial paths and generalized majorizations, Electron. J. Combin., 17 (1) (2010), R61. [6] M. Dodig, M. Stošić, On properties of the generalized majorization, Electron. J. Linear Algebra, 26 (2013), 471-509. [7] F. R. Gantmacher, Matrix theory, Vol. 1 and 2, Chelsea, New York, 1974. [8] Y. Han, Subrepresentations of Kronecker representations, Linear Algebra Appl


We treat the boundary of the union of blocks in the Jenga game as a surface with a polyhedral structure and consider its genus. We generalize the game and determine the maximum genus among the configurations in the generalized game.



The Tangram is a puzzle in which seven tiles are arranged to make various shapes. Four families of tangram shapes have been mathematically defined and their members enumerated. This paper defines a fifth family, enumerates its members, explains its taxonomic relationship with the previously-defined families, and provides some interesting examples


Given a (symmetrically-moving) piece from a chesslike game, such as shogi, and an n×n board, we can form a graph with a vertex for each square and an edge between two vertices if the piece can move from one vertex to the other. We consider two pieces from shogi: the dragon king, which moves like a rook and king from chess, and the dragon horse, which moves like a bishop and rook from chess. We show that the independence number for the dragon kings graph equals the independence number for the queens graph. We show that the (independent) domination number of the dragon kings graph is n − 2 for 4 ≤ n ≤ 6 and n − 3 for n ≥ 7. For the dragon horses graph, we show that the independence number is 2n − 3 for n ≥ 5, the domination number is at most n−1 for n ≥ 4, and the independent domination number is at most n for n ≥ 5.