A new proof of Kiselman's minimum principle for plurisubharmonic functions

We give a new proof of Kiselman's minimum principle for plurisubharmonic functions, inspired by Demailly's regularization of plurisubharmonic functions by using Ohsawa–Takegoshi's extension theorem.     

An improvement of the inclusion-exclusion principle

We present an improvement of the inclusion-exclusion principle in which the number of terms is reduced by predicted cancellation. The improvement generalizes a related result of Narushima as well as a graph-theoretic theorem of Whitney. Applications concern chromatic polynomials of graphs and permanents of 0,1-matrices.     

A short proof of Kneser's conjecture

In the paper a short proof is given for Kneser's conjecture. The proof is based on Borsuk's theorem and on a theorem of Gale.     

A short proof of Minc's conjecture

A short proof is given of the following conjecture of Minc, proved in 1973 by Brègman. Let A be a n × n ? (0, 1)-matrix with r_i ones in row i. Then per .     

A simplified proof of parikh's theorem

A strengthened form of the pumping lemma for context-free languages is used to give a simple proof of Parikh's Theorem.     

Another proof of dilworth's decomposition theorem

Dilworth's famous theorem [1] states that if the maximal sized antichains of a finite poset X have n elements, then X can be covered by n chains. The number n is called the width of X. Apart from proofs relating the theorem to other key theorems of combinatorics (see [1–4]), there have been a number of direct proofs (see [1, 2, 5, 6]). The shortest of these is the one by Perles [5], the outline of which is as follows.     

A short proof of Meyniel's theorem

Meyniel's theorem states that a strict diconnected digraph has a directed Hamilton cycle if d(u) + d(v) ? 2n ? 1 for every pair u, v of nonadjacent vertices. We give short proof of this theorem.     

A bijective proof of the hook-length formula

A well-known theorem of Frame, Robinson, and, Thrall states that if λ is a partition of n, then the number of Standard Young Tableaux of shape λ is n! divided by the product of the hook-lengths. We give a new combinatorial proof of this formula by exhibiting a bijection between the set of unsorted Young Tableaux of shape λ, and the set of pairs (T, S), where T is a Standard Young Tableau of shape λ and S is a “Pointer” Tableau of shape λ.     

A bijective proof of the hook-length formula for skew shapes

Recently, Naruse presented a beautiful cancellation-free hook-length formula for skew shapes. The formula involves a sum over objects called excited diagrams, and the term corresponding to each excited diagram has hook lengths in the denominator, like the classical hook-length formula due to Frame, Robinson and Thrall. In this paper, we present a simple bijection that proves an equivalent recursive version of Naruse’s result, in the same way that the celebrated hook-walk proof due to Greene, Nijenhuis and Wilf gives a bijective (or probabilistic) proof of the hook-length formula for ordinary shapes.In particular, we also give a new bijective proof of the classical hook-length formula, quite different from the known proofs.     

An almost‐bijective proof of an asymptotic property of partitions

Let 𝒫_n be the set of all distinct ordered pairs (λ,λ_i), where λ is a partition of n and λ_i is a part size of λ. The primary result of this note is a combinatorial proof that the probability that, for a pair (λ,λ_i) chosen uniformly at random from 𝒫_n, the multiplicity of λ_i in λ is 1 tends to 1/2 as n →∞. This is inspired by work of Corteel, Pittel, Savage, and Wilf (Random Structures and Algorithms 14 (1999), 185–197). © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

Means,Milne’s inequality,and quadrilateral area

Aequationes mathematicae - We discuss Milne’s inequality and apply it to the sides of a convex quadrilateral to derive an approximation to the area of the quadrilateral via arithmetic and...     

Parallel summation,Maxwell's principle and the infimum of projections

In this paper we apply Maxwell's principle to give simple proofs of the properties of R: S, the parallel sum of two positive semi-definite linear operators. The parallel sum has been studied by Anderson, Ando, Duffin, Fillmore, Mitra, Williams, and others. In particular we give a short, elementary, and geometric proof of the result of Anderson and Duffin that gives the infimum of two orthogonal projections as twice their parallel sum.