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Cycles and sorting index for matchings and restricted permutations
Cycles and sorting index matchings and restricted permutations Combinatorics
2012/6/25
We prove that the Mahonian-Stirling pairs of permutation statistics $(\sor, \cyc)$ and $(\inv, \mathrm{rlmin})$ are equidistributed on the set of permutations that correspond to arrangements of $n$ no...
The Sorting Index and Permutation Codes
Permutation statistics Mahonian statistics Coxeter groups Set-valued statistics Bijections
2012/6/19
In the combinatorial study of the coefficients of a bivariate polynomial that generalizes both the length and the reflection length generating functions for finite Coxeter groups, Petersen introduced ...
Blocking Sets of Index Three
Redei Blocking Sets Projective Triangle Projective Triad Combinatorics
2012/6/15
In this note we will provide proofs for the various statements that have been made in the literature about blocking sets of index three. Our aim is to clarify what is known about the characterization ...
Heuristic and exact solutions to the inverse power index problem for small voting bodies
electoral systems simple games weighted voting games square root rule Penrose limit theorem
2012/2/29
Power indices are mappings that quantify the influence of the members of a voting body on collective decisions a priori. Their nonlinearity and discontinuity makes it difficult to compute inverse imag...
On augmented eccentric connectivity index of graphs and trees
eccentric connectivity index Combinatorics graphs and trees
2011/9/2
Abstract: In this paper we establish all extremal graphs with respect to augmented eccentric connectivity index among all (simple connected) graphs, among trees and among trees with perfect matching. ...
A Combined Logarithmic Bound on the Chromatic Index of a Multigraph
Combined Logarithmic Bound Chromatic Index of Multigraph
2011/2/25
For a multigraph G, the integer round-up (G) of the fractional chromatic index f (G) yields a good general lower bound for the chromatic index „ (G). For an upper bound,...