Related papers: The Third Trick

We discuss properties of recursive schemas related to McCarthy's ``91 function'' and to Takeuchi's triple recursion. Several theorems are proposed as interesting candidates for machine verification, and some intriguing open questions are…

We use a triple-point version of the Whitney trick to show that ornaments of three orientable $(2k-1)$-manifolds in $\mathbb R^{3k-1}$, $k>2$, are classified by the $\mu$-invariant. A very similar (but not identical) construction was found…

We prove the existence of a finite set of moves sufficient to relate any two representations of the same 3-manifold as a 4-fold simple branched covering of S^3. We also prove a stabilization result: after adding a fifth trivial sheet two…

We continue the work begun in OEIS sequence A332636 which presents recursive sequences that have triangles that appear embedded in them. This paper i) generalizes the main result presented in A332636, ii) provides a complete set of…

We survey the classical results of the Dirichlet Approximation Theorem.

In this article, we define a very important sequence of functions, all the functions of this sequence present behaviors very close to that of the Collatz function. The study of such functions allows us to obtain very interesting results…

In previous work with Mikhail Khovanov and Aaron Lauda we introduced two odd analogues of the Schur functions: one via the combinatorics of Young tableaux (odd Kostka numbers) and one via the odd symmetrization operator. In this paper we…

We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.

We give a new proof of a version of the main theorem of the previous paper in the series about embedding of an algebraic system into ultraproducts.

We develop a theory of multiplicative functions (with values inside or on the unit circle) in arithmetic progressions analogous to the well-known theory of primes in arithmetic progressions.

We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.

We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.

We present a new method to obtain infinite Sidon sequences, based on the discrete logarithm. We construct an infinite Sidon sequence A, with A(x)= x^{\sqrt 2-1+o(1)}. Ruzsa proved the existence of a Sidon sequence with similar counting…

This version of the paper corrects an inaccuracy in the proof of Theorem 2.9 in the published version. The main results remain unchanged.

We present the Sequent Calculus Trainer, a tool that supports students in learning how to correctly construct proofs in the sequent calculus for first-order logic with equality. It is a proof assistant fostering the understanding of all the…

The main result of the paper is a description of the class of functions on the unit circle, for which Krein's trace formula holds for arbitrary pairs of unitary operators with trace class difference. We prove that this class of functions…

CZF + Separation is shown to be equiconsistent with second-order arithmetic, using realizability.

We proved three theorems of $S$-version of the mulyiplicity one.

G3-style sequent calculi for the logics in the cube of non-normal modal logics and for their deontic extensions are studied. For each calculus we prove that weakening and contraction are height-preserving admissible, and we give a syntactic…

By investigating a recurrence relation about functions, we first give alternative proofs of various identities on Fibonacci numbers and Lucas numbers, and then, make certain well known identities visible via certain trivalent graph…