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math.CO updates on arXiv.org

Complement Submodular Information Measures for Balanced and Robust Data Selection A Proof of a Conjecture on Positive and Negative Square Energies of Unicyclic Graphs Laplacian Spectrum of the Weakly Zero-Divisor Graph of a Finite Commutative Ring An identity for second Eulerian numbers via lattice-point counting $t$-tone edge coloring of graphs Constructing Maximal Bumpless Pipedreams for Double Grothendieck Polynomials Mubayi's Polynomial-Ideal Conjecture and Cover-Ideal Turán Methods Implicit Binarization via Complex Phase Dynamics in Combinatorial Optimization The limits of Schur multipliers in Pólya conversion problems for the $q$-permanent function Universality theorems for generalized splines Framing Triangulations for Arbitrary Integer Flow Polytopes On the Common Generalization of Gentle Algebras and Framed Directed Acyclic Graphs The complexity of frugal digraph homomorphisms Chaotic and periodic behavior of jeu de taquin on infinite Young tableaux Enumerating Pattern Avoiding Parking Functions Incidence toric ideals and three-point functions Unique Winning Opening Move in Three-Row Chomp Strong majority colorings of graphs A Balancing Theorem for Spanning Trees of Rectangular Grid Graphs Spectral radius and edge-disjoint connected factors of graphs New invariants for rank metric codes, with applications to the classification of rank two semifields of order 256 Flexible DP-4-coloring of planar graphs without 4-cycles and intersecting triangles Balanced intersection size distributions in projective planes List Reconstruction Problem with List Size Two Is Dimensionality a Barrier for Retrieval Models? The INIEP: Irreducible and Positive Realizations The number of Pfaffian orientations on punctured polygonally cellulated surfaces Explicit Construction of Polytopes whose Ehrhart Polynomials Realize any Given Sign Pattern Finite-state enumeration of adjacency-constrained 132-avoiding permutations AMDS and quantum AMDS Constacyclic codes of length $4p^ς$ over $\mathbb{F}_{{p}^{m}}$
Determining the essentially different partitions of all J...
T. G. J. Beelen, T. Verhoeff · 2018-11-29 · via math.CO updates on arXiv.org

In this report we consider the set of the 16 possible convex tangrams that can be composed with the 7 so-called "Sei Shonagon Chie no Ita" (or Japanese) tans, see [10]. The set of these Japanese tans is slightly different from the well-known set of 7 Chinese tans with which 13 (out of those 16) convex tangrams can be formed. In [4], [6] the problem of determining all essentially different partitions of the 13 "Chinese" convex tangrams was investigated and solved. In this report we will address the same problem for the "Japanese" convex tangrams. The approach to solve both problems is more or less analogous, but the "Japanese" problem is much harder than the "Chinese" one, since the number of "Japanese" solutions is much larger than the "Chinese" ones. In fact, only for a few "Japanese" tangram shapes their solutions can be found by a rigorous analysis supported by a large number of clarifying diagrams. The solutions for the remaining shapes have to be determined using a dedicated computer program. Both approaches will be discussed here and all essentially different solutions with the "Japanese" tans are presented. As far as we know all presented results are not yet published before.