Related papers: A short proof of Isserlis' theorem

Approximations to the Kruskal-Katona theorem are stated and proven. These approximations are weaker than the theorem, but much easier to work with numerically.

This article concerns a class of beam equations with damping on rectangular tori. When the generators satisfy certain relationship, by excluding some value of two model parameters, we prove that such models admit small amplitude…

We prove a Torelli-like theorem for higher-dimensional function fields, from the point of view of "almost-abelian" anabelian geometry.

We prove the A-theoretic Isomorphism Conjecture with coefficients and finite wreath products for solvable groups.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

We prove an extension of the well-known combinatorial-topological lemma of E. Sperner to the case of infinite-dimensional cubes. It is obtained as a corollary to an infinitary extension of the Lebesgue Covering Dimension Theorem.

We give a short straightforward proof for the bound of the reminder term in the Taylor theorem. The proof uses only induction and the fact that $f'\geq 0$ implies the monotonicity of $f$, so it might be an attractive proof to give to…

In this paper we introduce a new method to produce lower bounds for the Waring rank of symmetric tensors. We also introduce the notion of $e$-computability and we use it to prove that Strassen's Conjecture holds in infinitely many new…

We present a relative form of the Toponogov comparison theorem.

Let $\mathcal E$ be a torus-linearised reflexive sheaf over a smooth projective toric variety. Generalising a theorem of Perlman and Smith, we prove an explicit sufficient condition for $\mathcal E$ to be acyclic via Weil decorations.

The paper gives a unified and simple proof of both theorems and Cousin's theorem.

We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…

Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.

It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.

Working from definitions and an elementarily obtained integral formula for the Euler-Mascheroni constant, we give an alternative proof of the classical Puiseux representation of the exponential integral.

In the present paper, we prove that two discrete rectangular tori are isospectral if and only if they are isomorphic.

In measure theory, Steinhaus theorem is a result that deals with a property of the difference between two sets of positive measure. We give a simple elementary proof of the result.

The Bollob\'as-Varopoulos theorem is an analogue of Hall's matching theorem on non-atomic measure spaces. Here we prove a finite version with a completely constructive proof.

We give q-analogues of Wilson's theorem for the primes congruent 1 and 3 modulo 4 respectively. And q-analogues of two congruences due to Mordell and Chowla are also established.