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1.
Secondary constructions of plateaued Boolean functions through addition of indicators
Enes Pašalić, Sadmir Kudin, Samir Hodžić, Dilawar Abbas Khan, 2026, izvirni znanstveni članek

Opis: Recently, the design of $s$-plateaued functions over $\F_2^n$, whose Walsh spectra take values in ${0,\pm 2^{\frac{n+s}{2}}}$, has been studied algorithmically to identify balanced plateaued functions of maximal algebraic degree, called optimal. In this article, we characterize optimal plateaued functions within the Generalized Maiorana-McFarland (GMM) class and provide sufficient conditions for them to have no nonzero linear structures. By adapting a technique of C. Carlet for modifying bent functions in the Maiorana-McFarland ($\cM$) class, we derive new classes of plateaued functions from $GMM$, including the subclass $\cD_0$ when $\phi$ is non-injective, although under more restrictive conditions. We also identify conditions ensuring plateauedness in the resulting $\cC$ class. Finally, using indicator functions of the form $1_{E_1}(x)1_{E_2}(y)$ for suitably chosen subspaces $E_1\subseteq\F_2^k$ and $E_2\subseteq\F_2^{n-k}$, we construct plateaued functions outside GMM.
Ključne besede: plateaued functions, linear structures, GMM class
Objavljeno v RUP: 19.08.2026; Ogledov: 321; Prenosov: 28
.pdf Celotno besedilo (373,64 KB)
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2.
Avoidability in graph theory : master’s thesis
Ina Bašić, 2026, magistrsko delo

Ključne besede: graph theory, avoidable structures, paths, trails, two-rooted graphs
Objavljeno v RUP: 20.03.2026; Ogledov: 719; Prenosov: 27
.pdf Celotno besedilo (537,14 KB)

3.
On the Q‐polynomial property of bipartite graphs admitting a uniform structure
Blas Fernández, Roghayeh Maleki, Štefko Miklavič, Giusy Monzillo, 2026, izvirni znanstveni članek

Ključne besede: subconstituent algebra, uniform posets, Q-polynomial structures
Objavljeno v RUP: 16.01.2026; Ogledov: 918; Prenosov: 5
.pdf Celotno besedilo (410,55 KB)
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