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Displaying 321 – 340 of 410

Some properties of Davenport-Schinzel sequences

D. Roselle, R. Stanton (1971)

Acta Arithmetica

Some properties of min-wise independent families and groups of permutations.

Bargachev, V. (2004)

Zapiski Nauchnykh Seminarov POMI

Some results on derangement polynomials

Mehdi Hassani, Hossein Moshtagh, Mohammad Ghorbani (2022)

Commentationes Mathematicae Universitatis Carolinae

We study moments of the difference $D_{n} (x) - x^{n} n! e^{- 1 / x}$ concerning derangement polynomials $D_{n} (x)$ . For the first moment, we obtain an explicit formula in terms of the exponential integral function and we show that it is always negative for $x > 0$ . For the higher moments, we obtain a multiple integral representation of the order of the moment under computation.

Some results on the $m (4)$ problem of Erdös and Hajnal.

Manning, Gregory M. (1995)

Electronic Research Announcements of the American Mathematical Society [electronic only]

Stable marriages. (Mariages stables.)

Dumont, Dominique (1990)

Séminaire Lotharingien de Combinatoire [electronic only]

Statistics on Dyck paths.

Mansour, Toufik (2006)

Journal of Integer Sequences [electronic only]

*-sturmian words and complexity

Izumi Nakashima, Jun-Ichi Tamura, Shin-Ichi Yasutomi (2003)

Journal de théorie des nombres de Bordeaux

We give analogs of the complexity $p (n)$ and of Sturmian words which are called respectively the $*$ -complexity $p_{*} (n)$ and $*$ -Sturmian words. We show that the class of $*$ -Sturmian words coincides with the class of words satisfying $p_{*} (n) \leq n + 1$ , and we determine the structure of $*$ -Sturmian words. For a class of words satisfying $p_{*} (n) = n + 1$ , we give a general formula and an upper bound for $p (n)$ . Using this general formula, we give explicit formulae for $p (n)$ for some words belonging to this class. In general, $p (n)$ can take large values, namely,...

Subsequence containment by involutions.

Jaggard, Aaron D. (2005)

The Electronic Journal of Combinatorics [electronic only]

Substitutions, abstract number systems and the space filling property

Clemens Fuchs, Robert Tijdeman (2006)

Annales de l’institut Fourier

In this paper we study multi-dimensional words generated by fixed points of substitutions by projecting the integer points on the corresponding broken halfline. We show for a large class of substitutions that the resulting word is the restriction of a linear function modulo $1$ and that it can be decided whether the resulting word is space filling or not. The proof uses lattices and the abstract number system associated with the substitution.

Substitutions on two letters, cutting segments and their projections

Sierk W. Rosema (2007)

Journal de Théorie des Nombres de Bordeaux

In this paper we study the structure of the projections of the finite cutting segments corresponding to unimodular substitutions over a two-letter alphabet. We show that such a projection is a block of letters if and only if the substitution is Sturmian. Applying the procedure of projecting the cutting segments corresponding to a Christoffel substitution twice results in the original substitution. This induces a duality on the set of Christoffel substitutions.