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A characterization of n-associative, monotone, idempotent functions on an interval that have neutral elements Kiss, Gergely ; 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 ▲] Detailed reference viewed: 116 (39 UL)Associative idempotent nondecreasing functions are reducible Kiss, Gergely ; in Semigroup Forum (2017) An n-variable associative function is called reducible if it can be written as a composition of a binary associative function. In this paper we summarize the known results when the function is defined on ... [more ▼] An n-variable associative function is called reducible if it can be written as a composition of a binary associative function. In this paper we summarize the known results when the function is defined on a chain and nondecreasing. The main result of this paper shows that associative idempotent and nondecreasing functions are uniquely reducible. [less ▲] Detailed reference viewed: 86 (9 UL)Generalization of Czoga\l a-Drewniak Theorem for $n$-ary semigroups Kiss, Gergely ; 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 ▲] Detailed reference viewed: 41 (3 UL)A characterisation of associative idempotent nondecreasing functions with neutral elements Kiss, Gergely ; ; Marichal, Jean-Luc et al Scientific Conference (2016, June) Detailed reference viewed: 86 (14 UL)Decomposition of balls in R^d Kiss, Gergely ; 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 ▲] Detailed reference viewed: 64 (3 UL)On the discrete Fuglede and Pompeiu problem Kiss, Gergely ; ; et al E-print/Working paper (n.d.) Detailed reference viewed: 45 (0 UL) |
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