Papers by Aleksandar Jurisic
Asociativne sheme prestavljajo enega izmed temeljev moderne kombinatorike. V tem sestavku z njimi... more Asociativne sheme prestavljajo enega izmed temeljev moderne kombinatorike. V tem sestavku z njimi obravnavamo prepletanje algebre in kombinatorike, ki je znano pod imenom algebraična kombinatorika. Gre za diskretno matematiko, kjer pa imajo objekti in strukture določeno stopnjo regularnosti. Pomembneǰsa področja praktičnih uporab algebraične kombinatorike so teorija kod za odpravljanje napak, teorija statističnega načrtovanja eksperimentov, ter prek končnih geometrij in končnih obsegov tudi kriptografija.
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European Journal of Combinatorics, 2010
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We obtain the following characterization of Q-polynomial distance-regular graphs. Let denote a di... more We obtain the following characterization of Q-polynomial distance-regular graphs. Let denote a distance-regular graph with diameter d> 3. Let E denote a minimal idempotent of which is not the trivial idempotent E_0. Let {θ_i^*}_i=0^d denote the dual eigenvalue sequence for E. We show that E is Q-polynomial if and only if (i) the entry-wise product E ∘ E is a linear combination of E_0, E, and at most one other minimal idempotent of ; (ii) there exists a complex scalar β such that θ^*_i-1-βθ^*_i + θ^*_i+1 is independent of i for 1 < i < d-1; (iii) θ^*_i θ^*_0 for 1 < i < d.
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We consider a distance-regular graph \Gamma with diameter d 3 and eigenvalues k =
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We prove the following bound for a k-regular graph on n vertices with nontrivial eigenvalues from... more We prove the following bound for a k-regular graph on n vertices with nontrivial eigenvalues from the interval [r; s] n(k + rs) (k \Gamma r)(k \Gamma s):
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Journal of Algebraic Combinatorics - J ALGEBR COMB, 2000
We consider a distance-regular graph Γ with diameter d ≥ 3 and eigenvalues k = θ0 > θ1 > ..... more We consider a distance-regular graph Γ with diameter d ≥ 3 and eigenvalues k = θ0 > θ1 > ... > θd. We show the intersection numbers a1, b1 satisfy
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Journal of Combinatorial Theory, Series B, 2005
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Designs, Codes and Cryptography, 2000
Let ? bea distance-regular graph with diameter d. For vertices x and y of ? at distancei, 1 = i =... more Let ? bea distance-regular graph with diameter d. For vertices x and y of ? at distancei, 1 = i = d, we define the setsCi(x,y) = ?i-1(x) ? ?(y), Ai(x,y) = ?i(x) ? ?(y) and Bi(x,y) = ?i+1(x) ? ?(y).Then we say ? has the CABj property,if the partition CABi(x,y) = {Ci(x,y),Ai(x,y),Bi(x,y)}of the local graph of y is equitable
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Journal of Combinatorial Theory, Series A, 2011
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Biljni Lekar Plant Doctor, 2010
Pojedine vrste sitnih sisara, među kojima se, na prvom mestu, mogu izdvojiti glodari i zečevi, u ... more Pojedine vrste sitnih sisara, među kojima se, na prvom mestu, mogu izdvojiti glodari i zečevi, u godinama sa povoljnim ekolokim uslovima, mogu prouzrokovati značajnija otećenja voćnjaka i rasadnika, a samim tim i veće ekonomske gubitke. U agroekosistemima koje ...
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arXiv: Combinatorics, 2009
We obtain the following characterization of $Q$-polynomial distance-regular graphs. Let $\G$ deno... more We obtain the following characterization of $Q$-polynomial distance-regular graphs. Let $\G$ denote a distance-regular graph with diameter $d\ge 3$. Let $E$ denote a minimal idempotent of $\G$ which is not the trivial idempotent $E_0$. Let $\{\theta_i^*\}_{i=0}^d$ denote the dual eigenvalue sequence for $E$. We show that $E$ is $Q$-polynomial if and only if (i) the entry-wise product $E \circ E$ is a linear combination of $E_0$, $E$, and at most one other minimal idempotent of $\G$; (ii) there exists a complex scalar $\beta$ such that $\theta^*_{i-1}-\beta \theta^*_i + \theta^*_{i+1}$ is independent of $i$ for $1 \le i \le d-1$; (iii) $\theta^*_i \ne \theta^*_0$ for $1 \le i \le d$.
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Elliptic curves also figured prominently in the recent proof of Fermat's Last Theorem by Andr... more Elliptic curves also figured prominently in the recent proof of Fermat's Last Theorem by Andrew Wiles. Originally pursued for purely aesthetic reasons, elliptic curves have recently been utilized in devising algorithms for factoring integers, primality proving, and in public-key cryptography. In this article, we aim to give the reader an introduction to elliptic curve cryptosystems, and to demonstrate why these systems provide relatively small block sizes, high-speed software and hardware implementations, and offer the highest strength-per-key-bit of any known public-key scheme.
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J Algebr Comb, 2003
Let be a graph with diameter d 2. Recall is 1-homogeneous (in the sense of Nomura) whenever for e... more Let be a graph with diameter d 2. Recall is 1-homogeneous (in the sense of Nomura) whenever for every edge xy of the distance partitionz V() (z, y) = i, (x, z) = j 0 i, j dis equitable and its para...
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Discrete Mathematics, Jun 28, 2010
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Journal of Combinatorial Theory Series a, Aug 1, 2008
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Dm, 2010
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Papers by Aleksandar Jurisic