Đặng Võ Phúc

A second counterexample to Singer's conjecture on the algebraic transfer

In this paper, we provide a second explicit counterexample to Singer's injectivity conjecture for the algebraic transfer in bidegree $(6, 6+40) = (6,46).$ This result corrects one of the main theorems in our recent preprint \cite[Theorem 2.5]{Phuc}. Exact computation gives a two-...

A second counterexample to Singer's conjecture on the algebraic transfer

In this paper, we provide a second explicit counterexample to Singer's injectivity conjecture for the algebraic transfer in bidegree $(6, 6+40) = (6,46).$ This result corrects one of the main theorems in our recent preprint \cite[Theorem 2.5]{Phuc}. Exact computation gives a two-...

WARING LENGTH TWO FOR THE SUPERINVOLUTIVE L’VOV–KAPLANSKY COUNTEREXAMPLE ON UPPER TRIANGULAR MATRICES

Abstract Let F $F$ upper F be an algebraically closed field of characteristic zero. Campedel, Fagundes and Ioppolo [‘Upper triangular matrices with superinvolution: identities and images of multilinear polynomials’, Bull. Braz. Math. Soc. (N.S.) 57 (2026), Article no. 27] recentl...

Exact invariant computations and Singer's conjecture for three degree families in rank four

W. Singer's conjecture asserts that the algebraic transfer is injective in every bidegree. In this article, we establish this conjecture in rank four for the three infinite families of degrees $5\cdot2^r-2$, $17\cdot2^r-2$, and $2^{r+s+u}+2^{r+s}+2^s-3$, with all parameters posit...

Exact invariant computations and Singer's conjecture for three degree families in rank four

W. Singer's conjecture asserts that the algebraic transfer is injective in every bidegree. In this article, we establish this conjecture in rank four for the three infinite families of degrees $5\cdot2^r-2$, $17\cdot2^r-2$, and $2^{r+s+u}+2^{r+s}+2^s-3$, with all parameters posit...

Exact invariant computations and Singer's conjecture for three degree families in rank four

W. Singer's conjecture asserts that the algebraic transfer is injective in every bidegree. In this article, we establish this conjecture in rank four for the three infinite families of degrees $5\cdot2^r-2$, $17\cdot2^r-2$, and $2^{r+s+u}+2^{r+s}+2^s-3$, with all parameters posit...

Exact invariant computations and Singer's conjecture for three degree families in rank four

W. Singer's conjecture asserts that the algebraic transfer is injective in every bidegree. In this article, we establish this conjecture in rank four for the three infinite families of degrees $5\cdot2^r-2$, $17\cdot2^r-2$, and $2^{r+s+u}+2^{r+s}+2^s-3$, with all parameters posit...

Exact invariant computations and Singer's conjecture for three degree families in rank four

W. Singer's conjecture asserts that the algebraic transfer is injective in every bidegree. In this article, we establish this conjecture in rank four for the three infinite families of degrees $5\cdot2^r-2$, $17\cdot2^r-2$, and $2^{r+s+u}+2^{r+s}+2^s-3$, with all parameters posit...

Explicit cohit bases in the five-variable degrees $3\cdot2^s-3$

The Peterson hit problem, which asks for a minimal generating set of the polynomial algebra over the mod-$2$ Steenrod algebra, remains notoriously open for $k \geq 5$ variables. A fundamental reduction strategy narrows the problem to generic degree families $n$ satisfying the con...