Related papers: Proof of Irvine's Conjecture via Mechanized Guessi…
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 present two related conjectures, arising in work on i-matchings in random r-regular bipartite graphs. The conjectures themselves are easily stated and involve only basic properties of convergent power series. One formulation involves…
Recently, Z. W. Sun introduced a sequence $(S_n)_{n\geq 0}$, where $S_n=\frac{\binom{6n}{3n} \binom{3n}{n}}{2(2n+1)\binom{2n}{n}}$, and found one congruence and two convergent series on $S_n$ by {\tt{Mathematica}}. Furthermore, he proposed…
We prove a multivariable elliptic analogue of Jackson's 8W7 summation formula, which was recently conjectured by S.O.Warnaar.
Revised proofs of Kenneth Arrow's impossibility theorem have been presented in prose form, incorporating novel ideas such as decisive sets and pivotal voters. This study develops another approach to proving the theorem. Using a proof…
We present a new proof of Witten's conjecture. The proof is based on the analysis of the relationship between intersection indices on moduli spaces of complex curves and Hurwitz numbers enumerating ramified coverings of the 2-sphere.
We prove a new theorem on additive Levy processes and show that this theorem implies several proved theorems and a hard conjectured theorem.
We prove an instance of the cyclic sieving phenomenon in non-crossing connected graphs, as conjectured by S.-P. Eu.
We present a case study in {\it experimental} yet {\it rigorous} mathematics by describing an algorithm, fully implemented in both Mathematica and Maple, that {\it automatically conjectures}, and then {\it automatically proves}, closed-form…
We give a new proof of some cases of the Baum-Connes conjecture along the lines of a proof of the Farrell-Jones conjecture.
We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.
We prove three conjectures, related to the paperfolding sequence, in a recent paper [arXiv:2005.04066] of P. Barry.
Theorem proving is one of the oldest applications which require heuristics to prune the search space. Invertible proof procedures has been the major tool. In this paper, we present a novel and powerful heuristic called $nongshim$ which can…
(l) I have enough evidence to render the sentence S probable. (la) So, relative to what I know, it is rational of me to believe S. (2) Now that I have more evidence, S may no longer be probable. (2a) So now, relative to what I know, it is…
We consider the task of automated theorem proving, a key AI task. Deep learning has shown promise for training theorem provers, but there are limited human-written theorems and proofs available for supervised learning. To address this…
In a very celebrated paper A. Connes has formulated a conjecture which is now one of the most important open problem in Operator Algebras. This importance comes from the works of many mathematicians who have found some unexpected equivalent…
Transformation formulas for four-parameter refinements of the q-trinomial coefficients are proven. The iterative nature of these transformations allows for the easy derivation of several infinite series of q-trinomial identities, and can be…
We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle.
We present in this paper a new method to deal with automatic sequences. This method allows us to prove a M\"obius-randomness-principle for automatic sequences from which we deduce the Sarnak conjecture for this class of sequences.…
A proof of Sendov's conjecture is given.