相关论文: Notes on the multiplicity conjecture

Several results about the union-closed sets conjecture are presented.

We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…

We give some results and conjectures about recurrence relations for certain sequences of binomial sums.

These are some notes on the two Milnor conjectures and their proofs (due to Voevodsky, Orlov-Vishik-Voevodsky, and Morel).

This note is the follow up to a paper by M. Waldschmidt.

Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.

In this note we refine the alternativity in some bifurcation theorems of Rabinowitz type, and then improve a few of results in Lu (2022) [17].

An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.

Certain new inequalities for the sums of factorials are presented.

We prove some extensions of Andrews inequality.

I review the classical theory of likelihood based inference and consider how it is being extended and developed for use in complex models and sampling schemes.

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

We present a new conjecture for the $SU_q(N)$ Perk-Schultz models. This conjecture extends a conjecture presented in our article (Alcaraz FC and Stroganov YuG (2002) J. Phys. A vol. 35 pg. 6767-6787, and also in cond-mat/0204074).

We obtain new partial results supporting the spectral set conjecture in dimension 1.

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

In this note we show that the known relation between double groupoids and matched pairs of groups may be extended, or seems to extend, to the triple case. The references give some other occurrences of double groupoids.

This note imparts heuristic arguments and theorectical evidences that contradict the abc conjecture over the rational numbers. In addition, the rudimentary datails for transforming this problem into the doimain of equidistribution theory…

The note complements topological aspects of the theory of chiral algebras.

In this paper, we pose many challenging conjectures on congruences involving binomial coefficients and Ap\'ery-like numbers.

I discuss the computational methods behind the formulation of some conjectures related to variants on Andrews' $q$-Dyson conjecture.