46 citations · 71 across the 14 of their papers we have counts for
17 papers
About Some Relatives of Palindromes
Viorel Nitica, Andrei Török
We introduce two new classes of integers. The first class consists of numbers for which there exists at least one nonnegative integer , such that the sum of and the sum…
Infinite sets of -additive and -multiplicative Ramanujan-Hardy numbers
Viorel Nitica
Let be a numeration base. A -additive Ramanujan-Hardy number is an integer for which there exists at least an integer , called additive multiplier, such that the prod…
High degree -Niven numbers
Viorel Nitica
Let be a numeration base. A -Niven number is one that is divisible by the sum of its base digits. We introduce high degree -Niven numbers. These are -Niven numbers…
About Some Relatives of the Taxicab Number
Viorel Nitica
The taxicab number, , has the following property. If we add its digits we obtain . The number obtained from by reversing the order of its digits is . If we multi…
The tilings of deficient squares by ribbon L-tetrominoes are diagonally cracked
Viorel Nitica
We consider tilings of deficient rectangles by the set of ribbon -tetrominoes. A tiling exists iff the rectangle is a square of odd side. The missing cell is on…
Signed tilings by ribbon L n-ominoes, n even, via Groebner bases
Kenneth Gill, Viorel Nitica
Let be the set of ribbon -shaped -ominoes for some even, and let be with an extra square. We investigat…
Signed tilings by ribbon L n-ominoes, n odd, via Groebner bases
Viorel Nitica
We show that a rectangle can be signed tiled by ribbon L n-ominoes, n odd, if and only if it has a side divisible by n. A consequence of our technique, based on the exhibition of a…
A rigidity property of ribbon L-shaped n-ominoes and generalizations
Viorel Nitica
Let n integer greater or equal to 4 and even and let T_n be the set of ribbon L-shaped n-ominoes. We study tiling problems for regions in a square lattice by T_n. Our main result s…
The Geometric Structure of Max-Plus Hemispaces
Daniel Ehrmann, Zach Higgins, Viorel Nitica
Given a set S endowed with a convexity structure, a hemispace is a convex subset of S which has convex complement. We recall that R^n_{max} is a semimodule over the max-plus semifi…
Semigroup Conjectures for Central Semidirect Product of R^n with R^m
Kevin Lui, Viorel Nitica, Siddharth Venkatesh
In this paper we prove two new results about closed semigroups in the family of solvable groups H_{mn} that are semidirect products of R^m and R^n, and for which the structure homo…
On the dimension of max-min convex sets
Viorel Nitica, Sergei Sergeev
We introduce a notion of dimension of max-min convex sets, following the approach of tropical convexity. We introduce a max-min analogue of the tropical rank of a matrix and show t…
Tropical convexity over max-min semiring
Viorel Nitica, Sergei Sergeev
This is a survey on an analogue of tropical convexity developed over the max-min semiring, starting with the descriptions of max-min segments, semispaces, hyperplanes and an accoun…
Extended-valued topical and anti-topical functions on semimodules
Ivan Singer, Viorel Nitica
In previous papers we have studied topical functions f:X-> K and related classes of functions, where X is a b-complete semimodule over an idempotent b-complete semifield K. Without…
Characterization of tropical hemispaces by (P,R)-decompositions
Ricardo D. Katz, Viorel Nitica, Sergei Sergeev
We consider tropical hemispaces, defined as tropically convex sets whose complements are also tropically convex, and tropical semispaces, defined as maximal tropically convex sets…
Best approximation in max-plus semimodules
Marianne Akian, Stephane Gaubert, Viorel Nitica +1
We establish new results concerning projectors on max-plus spaces, as well as separating half-spaces, and derive an explicit formula for the distance in Hilbert's projective metric…
An interval version of separation by semispaces in max-min convexity
Viorel Nitica, Sergei Sergeev
We study separation of a closed box from a max-min convex set by max-min semispace. This can be regarded as an interval extension of known separation results. We give a constructiv…
On hyperplanes and semispaces in max-min convex geometry
Viorel Nitica, Sergei Sergeev
The concept of separation by hyperplanes is fundamental for convex geometry and its tropical (max-plus) analogue. However, analogous separation results in max-min convex geometry a…