Multiple gcd-closed sets and determinants of matrices associated with arithmetic functions

Siao Hong; Shuangnian Hu; Shaofang Hong

Displaying similar documents to “Multiple gcd-closed sets and determinants of matrices associated with arithmetic functions”

Determinant and inverse of meet and join matrices.

Altinisik, Ercan, Tuglu, Naim, Haukkanen, Pentti (2007)

International Journal of Mathematics and Mathematical Sciences

Similarity:

Notes on the divisibility of GCD and LCM matrices.

Haukkanen, Pentti, Korkee, Ismo (2005)

International Journal of Mathematics and Mathematical Sciences

Similarity:

On Zeilberger's constant term for Andrew's TSSCPP theorem.

Xin, Guoce (2011)

The Electronic Journal of Combinatorics [electronic only]

Similarity:

A Pfaffian-Hafnian analogue of Borchardt's identity.

Ishikawa, Masao, Kawamuko, Hiroyuki, Okada, Soichi (2005)

The Electronic Journal of Combinatorics [electronic only]

Similarity:

A representation theorem for operators on a space of interval functions.

Chatfield, J.A. (1978)

International Journal of Mathematics and Mathematical Sciences

Similarity:

A note on some new refinements of Jensen's inequality for convex functions.

Wang, Liang-Cheng, Ma, Xiu-Fen, Liu, Li-Hong (2009)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Similarity:

Determinants of matrices associated with incidence functions on posets

Shaofang Hong, Qi Sun (2004)

Czechoslovak Mathematical Journal

Similarity:

Let $S = {x_{1}, \dots, x_{n}}$ be a finite subset of a partially ordered set $P$ . Let $f$ be an incidence function of $P$ . Let $[f (x_{i} \land x_{j})]$ denote the $n \times n$ matrix having $f$ evaluated at the meet $x_{i} \land x_{j}$ of $x_{i}$ and $x_{j}$ as its $i, j$ -entry and $[f (x_{i} \lor x_{j})]$ denote the $n \times n$ matrix having $f$ evaluated at the join $x_{i} \lor x_{j}$ of $x_{i}$ and $x_{j}$ as its $i, j$ -entry. The set $S$ is said to be meet-closed if $x_{i} \land x_{j} \in S$ for all $1 \leq i, j \leq n$ . In this paper we get explicit combinatorial formulas for the determinants of matrices $[f (x_{i} \land x_{j})]$ and $[f (x_{i} \lor x_{j})]$ on any meet-closed set $S$ . We also obtain necessary and sufficient conditions for...

An analysis of GCD and LCM matrices via the $L D L^{T}$ -factorization.

Ovall, Jeffrey S. (2004)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Similarity:

Inequality-sum : a global constraint capturing the objective function

Jean-Charles Régin, Michel Rueher (2005)

RAIRO - Operations Research - Recherche Opérationnelle

Similarity:

This paper introduces a new method to prune the domains of the variables in constrained optimization problems where the objective function is defined by a sum $y = Σ x_{i}$ , and where the integer variables $x_{i}$ are subject to difference constraints of the form $x_{j} - x_{i} \leq c$ . An important application area where such problems occur is deterministic scheduling with the mean flow time as optimality criteria. This new constraint is also more general than a sum constraint defined on a set of ordered variables. Classical...