1. A Fourier–Jacobi Dirichlet series for cusp forms on orthogonal groupsRafail Psyroukis, 2025, izvirni znanstveni članek Opis: We investigate a Dirichlet series involving the Fourier-Jacobi coefficients of two cusp forms (F,G) for orthogonal groups of signature ((2,n+2)). In the case when (F) is a Hecke eigenform and (G) is a Maass lift of a Poincaré series, we establish a connection with the standard (L)-function attached to (F). What is more, we find explicit choices of orthogonal groups, for which we obtain a clear-cut Euler product expression for this Dirichlet series. Through our considerations, we recover a classical result for Siegel modular forms, first introduced by Kohnen and Skoruppa, but also provide a range of new examples, which can be related to other kinds of modular forms, such as paramodular, Hermitian, and quaternionic.
Ključne besede: orthogonal modular forms, Fourier-Jacobi forms, L-functions
Objavljeno v RUP: 25.09.2026; Ogledov: 201; Prenosov: 7
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3. Secondary constructions of plateaued Boolean functions through addition of indicatorsEnes 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: 439; Prenosov: 44
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4. Centrality in connected graphs via convexity or concavityDinesh Pandey, Kamal Lochan Patra, 2026, izvirni znanstveni članek Opis: In graph theory, several central parts of graphs have been defined. The center, median and the security center are three such concepts defined for any connected graph, while others are specific to trees. These definitions typically involve a function defined on the vertex set of the graph.
This paper generalizes the concepts of convex and concave functions, originally defined for trees, to connected graphs. Using this, we provide a unified approach to prove the known results that each of the center, median, and security center of a connected graph is either a cut vertex or lies within a block. Additionally, we introduce three new central parts of a connected graph as generalizations of the subtree core, core vertices, and characteristic set of a tree, and examine their properties in relation to the center, median, and security center. We also show that for any graph G, there exists a supergraph G' such that the subgraph induced by the characteristic center of G' is isomorphic to G. Finally, we propose several open problems related to subgraph core and core center.
Ključne besede: Center, characteristic center, convex and concave functions, core center, median, security center, subgraph core
Objavljeno v RUP: 17.08.2026; Ogledov: 342; Prenosov: 9
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6. Permutations satisfying (▫$P_1$▫) and (▫$P_2$▫) properties and ▫$\ell$▫-optimal bent functionsSadmir Kudin, Enes Pašalić, Alexandr Polujan, Fengrong Zhang, Haixia Zhao, 2026, izvirni znanstveni članek Opis: An important classification of permutations over Fm 2 , suitable for construct- ing Maiorana-McFarland bent functions on Fm 2 × Fm 2 with the unique M-subspace of maximal dimension, was recently considered in Pasalic et al (IEEE Trans Inf Theory 70:4464–4477, 2024). More precisely, two properties called (P1) and (P2) were in- troduced and a generic method of constructing permutations having the property (P1) was presented, whereas no such results were provided related to the (P2) property. In this article, we provide a deeper insight on these properties, their mutual relationship, and specify some explicit classes of permutations having these properties. Such per- mutations are then employed to generate a large variety of bent functions outside the completed Maiorana-McFarland class M# . We also introduce -optimal bent functions as bent functions with the lowest possible linearity index; such functions can be consid- ered as opposite to Maiorana-McFarland bent functions. We give explicit constructions of -optimal bent functions within the D0 class, which in turn can be employed in cer- tain secondary constructions of bent functions (Zhang et al in Inf Comput 297:105149, 2024) for providing even more classes of bent functions that are provably outside M# . Moreover, we demonstrate that a certain subclass of D0 has an additional property of having only 5-valued spectra decompositions, similarly to the only result in this direction concerning monomial bent functions (Canteaut and Charpin in IEEE Trans Inf Theory 498:2004–2019, 2003). Finally, we generalize the so-called swapping variables method introduced in Pasalic et al. (IEEE Trans Inf Theory 70:4464–4477, 2024) which then allows us to specify much larger families of bent functions outside M# compared to Pasalic et al (IEEE Trans Inf Theory 70:4464–4477, 2024). In this way, we give a better explanation of the origin of bent functions in dimension eight, since the vast majority of them is outside M# , as indicated in Langevin and Leander (Designs Codes Cryptogr 59:193–205, 2011).
Ključne besede: bent functions, Maiorana-McFarland class, permutations
Objavljeno v RUP: 30.12.2025; Ogledov: 1601; Prenosov: 12
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7. Almost Maiorana-McFarland bent functionsSadmir Kudin, Enes Pašalić, Alexandr Polujan, Fengrong Zhang, Haixia Zhao, 2025, izvirni znanstveni članek Opis: In this article, we study bent functions on F2m 2 of the form f (x, y) = x·φ(y)+h(y), where x ∈ Fm−1 2 and y ∈ Fm+1 2 , which form the generalized Maiorana-McFarland class (denoted by GMMm+1) and are referred to as almost Maiorana-McFarland bent functions. We provide a complete characterization of the bent property for such functions and determine their duals. Specifically, we show that f is bent if and only if the mapping φ partitions Fm+1 2 into 2-dimensional affine subspaces, on each of which the function h has odd weight. While the partition of Fm+1 2 into 2-dimensional affine subspaces is crucial for the bentness, we demonstrate that the algebraic structure of these subspaces plays an even greater role in ensuring that the constructed bent func- tions f are excluded from the completed Maiorana-McFarland class M# (the set of bent functions that are extended-affine equivalent to bent functions from the Maiorana-McFarland class M). Consequently, we investigate which properties of mappings φ : Fm+1 2 → Fm−1 2 lead to bent functions of the form f (x, y) = x · φ(y) + h(y) both inside and outside M# and provide construction methods for suitable Boolean functions h on Fm+1 2 . As part of this framework, we present a simple algorithm for constructing partitions of the vector space Fm+1 2 together with appropriate Boolean functions h that generate bent functions outside M#. When 2m = 8, we explicitly identify many such partitions that produce at least 278 distinct bent functions on F8 2 that do not belong to M#, thereby generating more bent functions outside M# than the total number of 8-variable bent functions in M# (whose cardinality is approximately 277). Additionally, we demonstrate that concatenating four almost Maiorana-McFarland bent functions outside M#, i.e., defining f = f1|| f2|| f3|| f4 where fi < M#, can result in a bent function f ∈ M#. This finding essentially answers an open problem posed recently in Kudin et al. (IEEE Trans. Inf. Theory 71(5): 3999- 4011, 2025). Conversely, using a similar approach to concatenate our functions f1|| f2|| f3|| f4, where each fi ∈ M#, we generate bent functions that are provably outside M#.
Ključne besede: bent functions, Maiorana-McFarland class, M-subspaces
Objavljeno v RUP: 29.12.2025; Ogledov: 1166; Prenosov: 10
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8. Vectorial negabent concepts : similarities, differences, and generalizationsNurdagül Anbar, Sadmir Kudin, Wilfried Meidl, Enes Pašalić, Alexandr Polujan, 2025, izvirni znanstveni članek Opis: In Pasalic et al. (IEEE Trans Inf Theory 69:2702–2712, 2023), and in Anbar and Meidl (Cryptogr Commun 10:235–249, 2018), two different vectorial negabent and vectorial bent- negabent concepts are introduced, which leads to seemingly contradictory results. One of the main motivations for this article is to clarify the differences and similarities between these two concepts. Moreover, the negabent concept is extended to generalized Boolean functions from Fn 2 to the cyclic group Z2k . It is shown how to obtain nega-Z2k -bent functions from Z2k -bent functions, or equivalently, corresponding non-splitting relative difference sets from the splitting relative difference sets. This generalizes the shifting results for Boolean bent and negabent functions. We finally point to constructions of Z8 -bent functions employing per- mutations with the (Am ) property, and more generally we show that the inverse permutation gives rise to Z2k -bent functions.
Ključne besede: bent function, Maiorana-McFarland class, negabent functions
Objavljeno v RUP: 12.09.2025; Ogledov: 1235; Prenosov: 50
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10. Konstrukcije novih superrazredov ukrivljenih funkcij in nadaljnje konstrukcije kriptografsko pomembnih preslikav izven M# : doktorska disertacijaAmar Bapić, 2022, doktorska disertacija Ključne besede: vecotorial bent function, class inclusion, complete Maiorana-McFaralnd class, MNBC functions, secondary constructions, weakly/almost strongly/strongly outside M#, 4-decomposition, SC and CD class, direct and indirect sum
Objavljeno v RUP: 12.12.2022; Ogledov: 4894; Prenosov: 54
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