Hasil untuk "cs.DM"

Mayer Goldberg

This work presents and extends a known spigot-algorithm for computing square-roots, digit-by-digit, that is suitable for calculation by hand or an abacus, using only addition and subtraction. We offer an elementary proof of correctness for the original algorithm, then present a corresponding spigot-algorithm for computing cube-roots. Finally, we generalize the algorithm, so as to find $r$-th roots, and show how to optimize the algorithm for any $r$. The resulting algorithms require only integer addition and subtraction.

Vesa Halava, Tero Harju, Teemu Pirttimäki

We show that there exists a fixed recursive function $e$ such that for all functions $h\colon \mathbb{N}\to \mathbb{N}$, there exists an injective function $c_h\colon \mathbb{N}\to \mathbb{N}$ such that $c_h(h(n))=e(c_h(n))$, i.e., $h=c_h^{-1}ec_h$.

Mikhail Starostin

Implicit expressability was introduced by A.V. Kuznetsov in 1979 as generalization of functional expressability. Set of functions is called implicitly complete if any function has an implicit representation over this set. The system of all implicitly maximal classes in three-valued logic is described. The implicit completeness criterion is stated.

Levon Aslanyan, Hasmik Sahakyan

Implementation details of method of monotone recognition, based on partitioning of the grid into the discrete structures isomorphic to binary cubes is presented.

Maurice Margenstern

In this paper, we prove that there is a strongly universal cellular automaton in the dodecagrid, the tessellation {5,3,4} of the hyperbolic 3D-space, with five states which is rotation invariant. This improves a previous paper of the author where the automaton required ten states.

Ian Parberry

New algorithms for generating closed knight's tours are obtained by generating a vertex-disjoint cycle cover of the knight's graph and joining the resulting cycles. It is shown experimentally that these algorithms are significantly faster in practice than previous methods. A fast obfuscation algorithm for closed knight's tours that obscures obvious artifacts created by their method of generation is also given, along with visual and statistical evidence of its efficacy.

Florian Barbero, Christophe Paul, Michal Pilipczuk

We prove that the strong immersion order is a well-quasi-ordering on the class of semi-complete digraphs, thereby strengthening a result of Chudnovsky and Seymour that this holds for the class of tournaments.

Johan De Wet, Susan Van Aardt

If $\mathcal{P}$ is a given graph property, we say that a graph $G$ is <i>locally</i> $\mathcal{P}$ if $\langle N(v) \rangle$ has property $\mathcal{P}$ for every $v \in V(G)$ where $\langle N(v) \rangle$ is the induced graph on the open neighbourhood of the vertex $v$. Pareek and Skupien (C. M. Pareek and Z. Skupien , On the smallest non-Hamiltonian locally Hamiltonian graph, J. Univ. Kuwait (Sci.), 10:9 - 17, 1983) posed the following two questions. <b>Question 1</b> Is 9 the smallest order of a connected nontraceable locally traceable graph? <b>Question 2</b> Is 14 the smallest order of a connected nontraceable locally hamiltonian graph? We answer the second question in the affirmative, but show that the correct number for the first question is 10. We develop a technique to construct connected locally hamiltonian and locally traceable graphs that are not traceable. We use this technique to construct such graphs with various prescribed properties.

Maurice Margenstern

In this paper, we construct a weakly universal cellular automaton on the tessellation $\{8,3\}$ which is not rotation invariant but which is truly planar.

Charles Sauerbier

A difference equation based method of determining two factors of a composite is presented. The feasibility of P-complexity is shown. Presentation of material is non-theoretical; intended to be accessible to a broader audience of non academic and theoretical practitioners.

Nilanjan De

In this study, the explicit expressions for F-index and coindex of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph (line graph of the subdivision graph) are obtained.

Masaki Watanabe

We use the modules introduced by Kraśkiewicz and Pragacz (1987, 2004) to show some positivity propertiesof Schubert polynomials. We give a new proof to the classical fact that the product of two Schubert polynomialsis Schubert-positive, and also show a new result that the plethystic composition of a Schur function with a Schubertpolynomial is Schubert-positive. The present submission is an extended abstract on these results and the full versionof this work will be published elsewhere.

Eugene Kuznetsov

Computer-based attempts to construct lower bounds for small Ramsey numbers are discussed. A systematic review of cyclic Ramsey graphs is attempted. Many known lower bounds are reproduced. Several new bounds are reported.

Meijie Ma

Wide diameter $d_ω(G)$ and fault-diameter $D_ω(G)$ of an interconnection network $G$ have been recently studied by many authors. We determine the wide diameter and fault-diameter of the integer simplex $T_m^n$. Note that $d_1(T_m^n)=D_1(T_m^n)= d(T_m^n)$, where $d(T_m^n)$ is the diameter of $T_m^n$. We prove that $d_ω(T_m^n)=D_ω(T_m^n)= d(T_m^n)+1$ when $2\leqω\leq n$. Since a triangular pyramid $TP_L$ is $T_L^3$, we have $d_ω(TP_L)=D_ω(TP_L)= d(TP_L)+1$ when $2\leqω\leq 3$.

Eric Blais, Li-Yang Tan, Andrew Wan

We give a new bound on the sum of the linear Fourier coefficients of a Boolean function in terms of its parity decision tree complexity. This result generalizes an inequality of O'Donnell and Servedio for regular decision trees. We use this bound to obtain the first non-trivial lower bound on the parity decision tree complexity of the recursive majority function.

Frédéric Havet, Andrew King

Graph Theory

Mahir Bilen Can, Yonah Cherniavsky

The purpose of this work is to initiate a combinatorial study of the Bruhat-Chevalley ordering on certain sets of permutations obtained by omitting the parentheses from their standard cyclic notation. In particular, we show that these sets form bounded, graded, unimodal, rank-symmetric and EL-shellable posets. Moreover, we determine the homotopy types of the associated order complexes.

Jean-Baptiste Priez

In a first part, we formalize the construction of combinatorial Hopf algebras from plactic-like monoids using polynomial realizations. Thank to this construction we reveal a lattice structure on those combinatorial Hopf algebras. As an application, we construct a new combinatorial Hopf algebra on binary trees with multiplicities and use it to prove a hook length formula for those trees.

Avinash J. Dalal, Jennifer Morse

We introduce two families of symmetric functions with an extra parameter $t$ that specialize to Schubert representatives for cohomology and homology of the affine Grassmannian when $t=1$. The families are defined by a statistic on combinatorial objects associated to the type-$A$ affine Weyl group and their transition matrix with Hall-Littlewood polynomials is $t$-positive. We conjecture that one family is the set of $k$-atoms.

Athma. M. Ram, R. Rama

A new algorithm to obtain the chromatic number of a finite, connected graph is proposed in this paper. The algorithm is based on contraction of non adjacent vertices.