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Displaying 641 – 660 of 849

The Wiener number of powers of the Mycielskian

Rangaswami Balakrishnan, S. Francis Raj (2010)

Discussiones Mathematicae Graph Theory

The Wiener number of a graph G is defined as $1 / 2 \sum_{u, v \in V (G)} d (u, v)$ , d the distance function on G. The Wiener number has important applications in chemistry. We determine a formula for the Wiener number of an important graph family, namely, the Mycielskians μ(G) of graphs G. Using this, we show that for k ≥ 1, $W (μ (S ₙ^{k})) \leq W (μ (T ₙ^{k})) \leq W (μ (P ₙ^{k}))$ , where Sₙ, Tₙ and Pₙ denote a star, a general tree and a path on n vertices respectively. We also obtain Nordhaus-Gaddum type inequality for the Wiener number of $μ (G^{k})$ .

The Wiener polynomial of the $k$ th power graph.

Abughneim, Omar A., Al-Ezeh, Hasan, Al-Ezeh, Mahmoud (2007)

International Journal of Mathematics and Mathematical Sciences

The wildcard set's size in the density Hales-Jewett theorem.

McCutcheon, Randall (2011)

The Electronic Journal of Combinatorics [electronic only]

The Young diagrams of a pair of irreducible characters of $S_{n}$ with the same zero set on $S_{n}^{ε}$ .

Belonogov, V.A. (2008)

Sibirskij Matematicheskij Zhurnal

The zeta function of a hypergraph.

Storm, Christopher K. (2006)

The Electronic Journal of Combinatorics [electronic only]

The $β$ -polynomials of complete graphs are real.

Li, Xueliang, Gutman, Ivan, Milovanović, V.Gradimir (2000)

Publications de l'Institut Mathématique. Nouvelle Série

Theorem proving through depth-first test

Zsolt Tuza (1992)

Acta Universitatis Carolinae. Mathematica et Physica

Théorèmes de Courant et de Cheng combinatoires

Yves Colin de Verdière (1994/1995)

Séminaire de théorie spectrale et géométrie

Theorems of the Nordhaus-Gaddum type for $k$ -uniform hypergraphs

František Olejník (1981)

Mathematica Slovaca

Théorie des magmoïdes

A. Arnold, M. Dauchet (1979)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Théorie des magmoïdes (I)

A. Arnold, M. Dauchet (1978)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Théorie des permutations et des arrangements circulaires complets

E. Jablonski (1892)

Journal de Mathématiques Pures et Appliquées

There are exactly 172 connected integral graphs up to 10 vertices.

Stanić, Zoran (2007)

Novi Sad Journal of Mathematics

There are no Golay complementary sequences of length 2.9t.

Malcolm Griffin (1977)

Aequationes mathematicae

There are ternary circular square-free words of length $n$ for $n \geq$ 18.

Currie, James D. (2002)

The Electronic Journal of Combinatorics [electronic only]

Theta functions, elliptic hypergeometric series, and Kawanaka's Macdonald polynomial conjecture.

Langer, Robin, Schlosser, Michael J., Warnaar, S.Ole (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Thin Lehman matrices and their graphs.

Wang, Jonathan (2010)

The Electronic Journal of Combinatorics [electronic only]

Thom polynomials and Schur functions: the singularities $I_{2, 2} (-)$

Piotr Pragacz (2007)

Annales de l’institut Fourier

We give the Thom polynomials for the singularities $I_{2, 2}$ associated with maps $(ℂ^{•}, 0) \to (ℂ^{• + k}, 0)$ with parameter $k \geq 0$ . Our computations combine the characterization of Thom polynomials via the “method of restriction equations” of Rimanyi et al. with the techniques of Schur functions.

Thom polynomials and Schur functions: the singularities $I I I_{2, 3} (-)$

Özer Öztürk (2010)

Annales Polonici Mathematici

We give a closed formula for the Thom polynomials of the singularities $I I I_{2, 3} (-)$ in terms of Schur functions. Our computations combine the characterization of the Thom polynomials via the “method of restriction equations” of Rimányi et al. with the techniques of Schur functions.

Thomas Harriot on Combinations

Ian Maclean (2005)

Revue d'histoire des mathématiques

Thomas Harriot (1560?–1621) is known today as an innovative mathematician and a natural philosopher with wide intellectual horizons. This paper will look at his interest in combinations in three contexts: language (anagrams), natural philosophy (the question of atomism) and mathematics (number theory), in order to assess where to situate him in respect of three current historiographical debates: 1) whether there existed in the late Renaissance two opposed mentalities, the occult and the scientific;...

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