An extension of the exponential formula in enumerative combinatorics.
An extension of the Foata map to standard Young tableaux.
An extension of the Ramanujan-Bailey formula. (Une extension d'une formule de Ramanujan-Bailey.)
An extremal characterization of projective planes.
An extremal problem for some classes of oriented graphs
An extremal problem on potentially -graphic sequences.
An extremal property of Turán graphs.
An extremal result for graphs with an application to their colourings.
An extremal theorem in the hypercube.
An identity between the determinant and the permanent of Hessenberg-type matrices
In this short note we provide an extension of the notion of Hessenberg matrix and observe an identity between the determinant and the permanent of such matrices. The celebrated identity due to Gibson involving Hessenberg matrices is consequently generalized.
An identity for fixed points of permutations.
An identity for the independence polynomials of trees.
An identity generator: basic commutators.
An identity in Rota-Baxter algebras.
An Implicit Weighted Degree Condition For Heavy Cycles
For a vertex v in a weighted graph G, idw(v) denotes the implicit weighted degree of v. In this paper, we obtain the following result: Let G be a 2-connected weighted graph which satisfies the following conditions: (a) The implicit weighted degree sum of any three independent vertices is at least t; (b) w(xz) = w(yz) for every vertex z ∈ N(x) ∩ N(y) with xy /∈ E(G); (c) In every triangle T of G, either all edges of T have different weights or all edges of T have the same weight. Then G contains...
An improved bound on the minimal number of edges in color-critical graphs.
An improved inductive definition of two restricted classes of triangulations of the plane
An improved tableau criterion for Bruhat order.
An improvement to Mathon's cyclotomic Ramsey colorings.
An inductive proof of Whitney's Broken Circuit Theorem
We present a new proof of Whitney's broken circuit theorem based on induction on the number of edges and the deletion-contraction formula.