Related papers: The choosability version of Brooks' theorem -- a s…

We prove a new version of Hall's Harem Theorem, where the final matching is realized by a unary function with additional conditions on behavior of cycles. The present paper can be considered as a helpful companion of the paper of the…

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem appears to be new but is closely related to results…

In this paper we show an index theorem for gerbes

We show in Bishop's constructive mathematics---in particular, using countable choice---that weak K\"{o}nig's lemma implies the uniform continuity theorem.

In this paper we present a surprisingly short proof of Minkowski's second theorem. The author hopes there is no mistake in it, though the argument seems to be too plain to contain one. Also, we apply the main construction of the proof to…

We derive the Gallai-Edmonds Structure Theorem from Hall's Theorem.

This note contains a newly streamlined version of the original proof that Outer space is contractible.

We give a simple proof of Dorronsoro's theorem and use similar ideas to establish an equivalence for embeddings of vector fields.

We give a short and self-contained proof of Levi's Extension Lemma for pseudoline arrangements.

The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…

In this paper, we present a short proof of Halin's grid theorem.

Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…

This note presents a simple proof of the characteristic function of Student's $t$-distribution. The method of proof, which involves finding a differential equation satisfied by the characteristic function, is applicable to many other…

The article provides a counterexample to a conjecture by Blocki-Zwonek.

This unpublished note is an alternate, shorter (and hopefully more readable) proof of the decidability of all minimal models. The decidability follows from a proof of the existence of a cellular term in each observational equivalence class…

We present a proof of the Sturm-Hurwitz theorem, using basic calculus.

We extract the Abhyankar-Moh-Suzuki theorem from the Lin-Zaidenberg theorem.

We prove the constructive version of Birkhoff's ergodic theorem following Vyugin but trying to separate and state explicitly the combinatorial statement on which this proof is based. We pose some questions related to this statement (and the…

We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.