### A Pfaffian-Hafnian analogue of Borchardt's identity.

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

The Electronic Journal of Combinatorics [electronic only]

Similarity:

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

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

The Electronic Journal of Combinatorics [electronic only]

Similarity:

Xin, Guoce (2011)

The Electronic Journal of Combinatorics [electronic only]

Similarity:

Papaschinopoulos, G., Schinas, C.J., Stefanidou, G. (2007)

Advances in Difference Equations [electronic only]

Similarity:

Zhongxue, Lü, Hongzheng, Xie (2002)

International Journal of Mathematics and Mathematical Sciences

Similarity:

Chatfield, J.A. (1978)

International Journal of Mathematics and Mathematical Sciences

Similarity:

Lowen, R., Verbeeck, C. (2003)

International Journal of Mathematics and Mathematical Sciences

Similarity:

Ivanka Tr. Angelova, Lubin G. Vulkov (2007)

Kragujevac Journal of Mathematics

Similarity:

Demetrovics, Janos, Thi, Vu Duc, Giang, Nguyen Long (2013)

Serdica Journal of Computing

Similarity:

There are limitations in recent research undertaken on attribute reduction in incomplete decision systems. In this paper, we propose a distance-based method for attribute reduction in an incomplete decision system. In addition, we prove theoretically that our method is more effective than some other methods.

Puninagool, W., Leeratanavalee, S. (2007)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

Similarity:

Shaofang Hong, Qi Sun (2004)

Czechoslovak Mathematical Journal

Similarity:

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

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

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

Similarity:

Afuwape, Anthony Uyi (1988)

International Journal of Mathematics and Mathematical Sciences

Similarity: