Related papers: On the WALA conjecture, Alberti representations an…
In this note we apply a substantial improvement of a result of S. Ferenczi on $S$-adic subshifts to give Bratteli-Vershik representations of these subshifts.
Using Easton collapses, we give a simplified construction of a model in which Chang's Conjecture for triples holds.
This paper is a successor of \cite{laceyt}. In that paper we considered bilinear operators of the form H_alpha(f_1,f_2)(x) = p.v. \int f_1(x-t) f_2(x + alpha t)/t dt, which are originally defined for f_1, f_2 in the Schwartz class S(R). The…
In this paper we will give a proof of a certain summation formula for Gamma functions utilizing Gegenbauer polynomials.
In this note, we provide bijective proofs of some identities involving the Bell number, as previously requested. Our arguments may be extended to yield a generalization in terms of complete Bell polynomials. We also provide a further…
We present a simple inductive proof of the Lagrange Inversion Formula.
This article presents an equivalent formulation of the implicit complementarity problem. We demonstrate that solution of the equivalent formulation is equivalent to the solution of the implicit complementarity problem. Moreover, we provide…
We study Milner's lambda-calculus with partial substitutions. Particularly, we show confluence on terms and metaterms, preservation of \b{eta}-strong normalisation and characterisation of strongly normalisable terms via an intersection…
A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.
We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…
In this paper we provide a full account of the Weil conjectures including Deligne's proof of the conjecture about the eigenvalues of the Frobenius endomorphism. Section 1 is an introduction into the subject. Our exposition heavily relies on…
We prove a local version of the Mazur-Ulam theorem.
I attempted to write the full translation of this article to make the remarkable proof of Pierre Deligne available to a greater number of people. Overviews of the proofs can be found elsewhere. I especially recommend the notes of James…
In the present note, we generalize the first part of the Borel-Cantelli lemma. By this generalization, we obtain some strong limit results.
We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…
First a few reformulations of Frankl's conjecture are given, in terms of reduced families or matrices, or analogously in terms of lattices. These lead naturally to a stronger conjecture with a neat formulation which might be easier to…
We provide the detailed proof of a strengthened version of the M. Artin Approximation Theorem.
We give a new proof of Carlitz-Wan's conjecture, previously proved by Lenstra (1995).Our proofs are natural and intuitive, and shed new insights into the study of exceptional polynomials.
We present a proof of the compositional shuffle conjecture, which generalizes the famous shuffle conjecture for the character of the diagonal coinvariant algebra. We first formulate the combinatorial side of the conjecture in terms of…
In this paper we consider iterated integrals of multiple polylogarithm functions and prove some explicit relations of multiple polylogarithm functions. Then we apply the relations obtained to find numerous formulas of alternating multiple…