A characterization of n-associative, monotone, idempotent functions on an interval that have neutral elements

in Semigroup Forum (2018)

We investigate monotone idempotent n-ary semigroups and provide a generalization of the Czogala–Drewniak Theorem, which describes the idempotent monotone associative functions having a neutral element. We ... [more ▼]

We investigate monotone idempotent n-ary semigroups and provide a generalization of the Czogala–Drewniak Theorem, which describes the idempotent monotone associative functions having a neutral element. We also present a complete characterization of idempotent monotone n-associative functions on an interval that have neutral elements. [less ▲]

Generalization of Czoga\l a-Drewniak Theorem for $n$-ary semigroups

in Torra, Vicenç; Mesiar, Radko; De Baets, Bernard (Eds.) Aggregation Functions in Theory and in Practice (2017)

We investigate n-ary semigroups as a natural generalization of binary semigroups. We refer it as a pair (X,F_n), where X is a set and an n-associative function F_n : X^n -> X is defined on X. We show that ... [more ▼]

We investigate n-ary semigroups as a natural generalization of binary semigroups. We refer it as a pair (X,F_n), where X is a set and an n-associative function F_n : X^n -> X is defined on X. We show that if F_n is idempotent, n-associative function which is monotone in each of its variables, defined on an interval I and has a neutral element, then F_n is combination of the minimum and maximum operation. Moreover we can characterize the n-ary semigroups (I,F_n) where F_n has the previous properties. [less ▲]

Decomposition of balls in R^d

in Mathematika (2016), 62(2), 378-405

We investigate the decomposition problem of balls into finitely many congruent pieces in dimension d = 2k. In addition, we prove that the d dimensional unit ball B_d can be divided into finitely many ... [more ▼]

We investigate the decomposition problem of balls into finitely many congruent pieces in dimension d = 2k. In addition, we prove that the d dimensional unit ball B_d can be divided into finitely many congruent pieces if d = 4 or d ≥ 6. We show that the minimal number of required pieces is less than 20d if d ≥ 10. [less ▲]