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    • Advances in nutrition (Bethesda, Md.) Journal

    Papers
    Misère Quotients for Impartial Games
    Thane E. Plambeck,Aaron N. Siegel
    Journal of Combinatorial Theory Series A（2007）
    We announce misère-play solutions to several previously-unsolved combinatorial games. The solutions are described in terms of misère quotients—commutative monoids that encode the additive structure of specific misère-play games. We also introduce several advances in the structure...
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    The Enumeration of C-Nets Via Quadrangulations
    R.C. Mullin,P.J. Schellenberg
    Journal of Combinatorial Theory（1968）
    A counting procedure for simple quadrangulations is established. Using the technique of counting simple quadrangulations together with a one-to-one correspondence between simple quadrangulations and c-nets, the enumeration of c-nets with i+1 vertices and j+1 faces is accomplished...
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    Block Configurations on Real Cubic Curves
    NS MENDELSOHN, R PADMANABHAN,B WOLK
    Journal of Combinatorial Theory Series A（1991）
    A 3k-block is a set of 3k points on a real non-singular cubic curve, which are the points of intersection of a real cubic curve and a curve of decree k. It has been proved [3]that 3k -I points on a real cubic curve uniquely determine- the remaining point of a 3k-block and that th...
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    Induced Subgraphs of Graphs with Large Chromatic Number. IV. Consecutive Holes
    Alex Scott,Paul Seymour
    Journal of Combinatorial Theory Series B（2018）
    A hole in a graph is an induced subgraph which is a cycle of length at least four. We prove that for all ν>0, every triangle-free graph with sufficiently large chromatic number contains holes of ν consecutive lengths.
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    Minimal Codes in Abelian Group Algebras
    RL MILLER
    Journal of Combinatorial Theory Series A（1979）
    In this paper we show that two minimal codes M1 and M2 in the group algebra F2[G] have the same (Hamming) weight distribution if and only if there exists an automorphism θ of G whose linear extension to F2[G] maps M1 onto M2. If θ(M1) = M2, then M1 and M2 are called equivalent. W...
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    A Semi-Finite Form of the Quintuple Product Identity
    Jun-Ming Zhu,Zhi-Zheng Zhang
    Journal of Combinatorial Theory Series A（2021）
    The quintuple product identity is deduced from the q-Dixon formula.
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    Designs from Pairs of Finite Fields. A Cyclic Unital U (6) and Other Regular Steiner 2-Designs
    S BAGCHI,B BAGCHI
    Journal of Combinatorial Theory Series A（1989）
    A general construction for Steiner 2-designs with prime power block size (and with a point-regular automorphism group) is presented. Its success depends on number-theoretic restrictions on the parameters—these are completely analysed in case of block sizes k ⩽ 11. The new designs...
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    The Minimal Number of Lines Intersected by a Set of Q + 2 Points, Blocking Sets, and Intersecting Circles
    A BLOKHUIS,AA BRUEN
    Journal of Combinatorial Theory Series A（1989）
    Lower bounds are given for the number of lines blocked by a set of q + 2 points in a projective plane of order q. Implications are discussed to the theory of blocking sets and bounds are obtained for the size of a double intersecting set of circles in a Möbius plane.
    Cited18Views0
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    A Complementation Theorem for Perfect Matchings of Graphs Having a Cellular Completion
    Mihai Ciucu
    Journal of Algebraic Combinatorics（1996）
    We introduce a family of graphs, called cellular, and consider the problem of enumerating their perfect matchings. We prove that the number of perfect matchings of a cellular graph equals a power of 2 times the number of perfect matchings of a certain subgraph, called the core of...
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    On the Combinatorics of String Polytopes
    Yunhyung Cho,Yoosik Kim,Eunjeong Lee,Kyeong-Dong Park
    Journal of Combinatorial Theory Series A（2021）
    For a reduced word i of the longest element in the Weyl group of SLn+1(C), one can associate the string cone Ci which parametrizes the dual canonical bases. In this paper, we classify all i's such that Ci is simplicial. We also prove that for any regular dominant weight λ of sln+...
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    A Generalization of Some Generalizations of Sperner's Theorem
    G.O.H Katona
    Journal of Combinatorial Theory, Series B（1972）
    A theorem of Erdös says: If A is a family of subsets of a set S of n elements and no h + 1 different members of the family form a chain A1 ⊂ … ⊂ An+1, then the maximum of the size of A is the sum of the h largest binomial coefficients of order n. The paper gives a weaker conditio...
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    Non-separating Induced Cycles in Graphs
    C THOMASSEN,B TOFT
    JOURNAL OF COMBINATORIAL THEORY SERIES B（1981）
    In this paper we consider non-separating induced cycles in graphs. A basic result is that any 2-connected graph with at least six vertices and without such a cycle has at least four vertices of degree 2, and this is best possible. For any 3-connected graph G we prove that there e...
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    Bijections among Combinatorial Models for Shifted Littlewood-Richardson Coefficients
    Seung-Il Choi,Sun-Young Nam,Young-Tak Oh
    Journal of Combinatorial Theory Series A（2014）
    We provide bijections among three combinatorial models for shifted Littlewood–Richardson coefficients; Littlewood–Richardson–Stembridge tableaux, λ-good semistandard decomposition tableaux, and shifted Littlewood–Richardson decomposition tableaux. To do this, we construct a bijec...
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    Maximal consistent families of triples
    Spencer, Joel
    Journal of Combinatorial Theory（1968）
    The general problem of dividing a set into a maximal collection of subsets in such a way that the subsets will overlap in certain specified ways is a fundamental problem in experimental design and in the design of systems involving shared use of system elements. This memorandum s...
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    Counting 3-Stack-sortable Permutations
    Colin Defant
    Journal of Combinatorial Theory Series A（2020）
    We prove a “decomposition lemma” that allows us to count preimages of certain sets of permutations under West's stack-sorting map s . As a first application, we give a new proof of Zeilberger's formula for the number W 2 ( n ) of 2-stack-sortable permutations in S n. Our proof ge...
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