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We show that every smooth manifold admits a smooth triangulation transverse to a given smooth map. This removes the properness assumption on the smooth map used in an essential way in Scharlemann's construction [5].
Homeomorphisms allowing us to prove topological equivalences between one-parameter families of maps undergoing the same bifurcation are constructed in this paper. This provides a solution for a classical problem in bifurcation theory that…
This article shines new light on the classical problem of tiling rectangles with squares efficiently with a novel method. With a twist on the traditional approach of resistor networks, we provide new and improved results on the matter using…
We provide a simple proof for the union-closed sets conjecture, a long-standing open problem in set theory with immediate applications to graph theory, number theory, and order-theory.
In this paper, we prove a conjecture by Aas and Linusson on the two-point correlations of adjacent particles in a continuous multispecies TASEP on a ring (AIHPD, 2018). We use the theory of multiline queues as devised by Ferrari and Martin…
Assuming a lower bound on the dimension, we prove a long standing conjecture concerning the classification of global solutions of the obstacle problem with unbounded coincidence sets.
Graceful tree conjecture is a well-known open problem in graph theory. Here we present a computational approach to this conjecture. An algorithm for finding graceful labelling for trees is proposed. With this algorithm, we show that every…
We prove three conjectures, related to the paperfolding sequence, in a recent paper [arXiv:2005.04066] of P. Barry.
In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].
As part of the recent developments in infinite matroid theory, there have been a number of conjectures about how standard theorems of finite matroid theory might extend to the infinite setting. These include base packing, base covering, and…
We prove effective versions of algebraic and analytic Lang's conjectures for product-quotient surfaces of general type with $P_g=0$ and $c_1^2=c_2$.
Barnette's Conjecture claims that all cubic, 3-connected, planar, bipartite graphs are Hamiltonian. We give a translation of this conjecture into the matching-theoretic setting. This allows us to relax the requirement of planarity to give…
We show constructively that, under certain regularity assumptions, any system of coupled linear differential equations with variable coefficients can be tridiagonalized by a time-dependent Lanczos-like method. The proof we present formally…
In this paper we introduce the notion of linear computability as a method of finding the Waring rank of forms. We use this notion to find infinitely many new examples which satisfy Strassen's Conjecture.
We propose a conjectural formula for $DR_g(a,-a) \lambda_g$ and check all its expected properties. Our formula refines the one point case of a similar conjecture made by the first named author in collaboration with Gu\'er\'e and Rossi, and…
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
In this paper we prove existence of matings between a large class of renormalizable cubic polynomials with one fixed critical point and another cubic polynomial having two fixed critical points. The resulting mating is a Newton map. Our…
We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.
In this paper we have given an algorithmic proof of an long standing Barnette's conjecture (1969) that every 3-connected bipartite cubic planar graph is hamiltonian. Our method is quite different than the known approaches and it rely on the…
In this paper, we give a proof of the DDVV conjecture which is a pointwise inequality involving the scalar curvature, the normal scalar curvature and the mean curvature on a submanifold of a real space form. Furthermore we solved the…