P. Stănică

activity

20002026

most citedOn the c-differential uniformity of certain maps over finite fields

41 citations · 136 across the 62 of their papers we have counts for

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18 papers · 1 filter

math.NT2026

Reduced APN permutations and a disproof of the Galois-ring lifting conjecture

Daniele Bartoli, Pantelimon Stanica

We construct infinite families of reduced almost perfect nonlinear (APN) permutations of $F_{2^{m}}$ that admit coefficientwise permutation lifts to $GR (2^{k}, m)$ for…

math.NT2026

Overconstrained character sums over finite abelian groups and decompositions of generalized bent, plateaued and landscape functions

Ayça Çeşmelioğlu, Constanza Riera, Pantelimon Stănică

Generalized bent (gbent) functions from an $n$ -variable Boolean space to $Z_{2^{k}}$ are central in cryptography and sequence design. Instead of the usual binary decompositi…

math.NT2026

Infinite families of APN permutations in constrained trivariate classes over $F_{2^{m}}$

Daniele Bartoli, Pantelimon Stanica

We study trivariate permutation polynomials over $F_{2^{m}}$ extending two APN permutation families of Li--Kaleyski (IEEE Trans. Inform. Theory, 2024) by allowing the scal…

math.NT2025

On the Classification of Dillon's APN Hexanomials

Daniele Bartoli, Giovanni Giuseppe Grimaldi, Pantelimon Stanica

We systematically analyze a class of hexanomial functions over finite fields of characteristic $2$ proposed by Dillon (2006) as candidates for almost perfect nonlinear (APN) functi…

math.NT2024

A proof of a conjecture on permutation trinomials

Daniele Bartoli, Mohit Pal, Pantelimon Stanica

In this paper we use algebraic curves and other algebraic number theory methods to show the validity of a permutation polynomial conjecture regarding $f(X)=X^{q(p-1)+1} +αX^{pq}+X^…

math.NT2024

Non-permutation phenomena in trivariate families over $\F_{2^m}$ and resolution of a conjecture

Daniele Bartoli, Mohit Pal, Pantelimon Stanica +1

Constructing permutation polynomials over finite fields, particularly those with simple algebraic structure in multiple variables, is a fundamental problem with applications in cry…

math.NT2023★ 1 cited

Representing the inverse map as a composition of quadratics in a finite field of characteristic $2$

Florian Luca, Santanu Sarkar, Pantelimon Stanica

In 1953, Carlitz~\cite{Car53} showed that all permutation polynomials over $\F_q$, where $q > 2$ is a power of a prime, are generated by the special permutation polynomials $x^{q - 2}$ …

math.NT2022

An infinite family of 0-APN monomials with two parameters

Nikolay Kaleyski, Kjetil Nesheim, Patenlimon Stănică

We consider an infinite family of exponents $e (l, k)$ with two parameters, $l$ and $k$ , and derive sufficient conditions for $e (l, k)$ to be 0-APN over $F_{2^{n}}$ . These cond…

math.NT2020

Low $c$ -differential and $c$ -boomerang uniformity of the swapped inverse function

Pantelimon Stanica

Modifying the binary inverse function in a variety of ways, like swapping two output points has been known to produce a $4$ -differential uniform permutation function. Recently, in…

math.NT2020★ 16 cited

The binary Gold function and its c-boomerang connectivity table

Sartaj Ul Hasan, Mohit Pal, Pantelimon Stanica

Here, we give a complete description of the c-Boomerang Connectivity Table for the Gold function over finite fields of even characteristic, by using double Weil sums. In the proces…

math.NT2020

Using double Weil sums in finding the $c$ -Boomerang Connectivity Table for monomial functions on finite fields

Pantelimon Stanica

In this paper we characterize the $c$ -Boomerang Connectivity Table (BCT), $c \neq = 0$ (thus, including the classical $c = 1$ case), for all monomial function $x^{d}$ in terms of characte…

math.NT2020

On the prime factors of the iterates of the Ramanujan $τ$ --function

Florian Luca, Sibusiso Mabaso, Pantelimon Stanica

In this paper, for a positive integer $n \geq 1$ , we look at the size and prime factors of the iterates of the Ramanujan $τ$ function applied to $n$ .

math.NT2015

On a divisibility relation for Lucas sequences

Yuri Bilu, Takao Komatsu, Florian Luca +2

In this note, we study the divisibility relation $U_{m} ∣ U_{n + k}^{s} - U_{n}^{s}$ , where $U := {U_{n}}_{n \geq 0}$ is the Lucas sequence of characteristic polynomial $x^{2} - a x \pm 1$ and $…

math.NT2008★ 1 cited

Minimal Niven numbers

H. Fredricksen, E. J. Ionascu, F. Luca +1

Define a(k,q) to be the smallest positive multiple of k such that the sum of its digits in base q is equal to k. The asymptotic behavior, lower and upper bound estimates of a(k,q)…

math.NT2006

Heron triangles with two fixed sides

Eugen J. Ionascu, Florian Luca, Pantelimon Stanica

In this paper, we study the function $H (a, b)$ , which associates to every pair of positive integers $a$ and $b$ the number of positive integers $c$ such that the triangle of sides $…

math.NT2003

On the prime power factorization of n!

Florian Luca, Pantelimon Stanica

In this paper we prove two results. The first theorem uses a paper of Kim \cite{K} to show that for fixed primes $p_{1}, ..., p_{k}$ , and for fixed integers $m_{1}, ..., m_{k}$ , with $p_i\not|…

math.NT2001

Products of Factorials Modulo p

Florian Luca, Pantelimon Stanica

A study of products of factorials modulo p and complete residues.

math.NT2000★ 1 cited

p^q-Catalan Numbers and Squarefree Binomial Coefficients

Pantelimon Stanica

In this paper we consider the generalized Catalan numbers F(s,n)= 1/((s-1)n+1) binom{sn}{n}. We find all $n$ such that for $p$ prime, p^q divides F(p^q,n), q>=1. As a byproduct we…

Reduced APN permutations and a disproof of the Galois-ring lifting conjecture

Overconstrained character sums over finite abelian groups and decompositions of generalized bent, plateaued and landscape functions

Infinite families of APN permutations in constrained trivariate classes over F2m​

On the Classification of Dillon's APN Hexanomials

A proof of a conjecture on permutation trinomials

Non-permutation phenomena in trivariate families over $\F_{2^m}$ and resolution of a conjecture

Representing the inverse map as a composition of quadratics in a finite field of characteristic 2

An infinite family of 0-APN monomials with two parameters

Low c-differential and c-boomerang uniformity of the swapped inverse function

The binary Gold function and its c-boomerang connectivity table

Using double Weil sums in finding the c-Boomerang Connectivity Table for monomial functions on finite fields

On the prime factors of the iterates of the Ramanujan τ--function

On a divisibility relation for Lucas sequences

Minimal Niven numbers

Heron triangles with two fixed sides

On the prime power factorization of n!

Products of Factorials Modulo p

p^q-Catalan Numbers and Squarefree Binomial Coefficients

Infinite families of APN permutations in constrained trivariate classes over $F_{2^{m}}$

Representing the inverse map as a composition of quadratics in a finite field of characteristic $2$

Low $c$ -differential and $c$ -boomerang uniformity of the swapped inverse function

Using double Weil sums in finding the $c$ -Boomerang Connectivity Table for monomial functions on finite fields

On the prime factors of the iterates of the Ramanujan $τ$ --function