Zobrazeno 1 - 10
of 86
pro vyhledávání: '"Martinjak, Ivica"'
Autor:
Martinjak, Ivica, Zubac, Ivana
Publikováno v:
Proceedings of the Croatian Combinatorial Days, 1, (2017) 53-63
The Gaussian polynomial in variable $q$ is defined as the $q$-analog of the binomial coefficient. In addition to remarkable implications of these polynomials to abstract algebra, matrix theory and quantum computing, there is also a combinatorial inte
Externí odkaz:
http://arxiv.org/abs/1712.07483
Autor:
Martinjak, Ivica, Škrekovski, Riste
We provide a combinatorial interpretation of Lah numbers by means of planar networks. Henceforth, as a conesquence of Lindstr\"om's lemma, we conclude that the related Lah matrix possesses a remarkable property of total non-negativity.
Comment:
Comment:
Externí odkaz:
http://arxiv.org/abs/1711.04547
Autor:
Martinjak, Ivica, Stanić, Dajana
The $n$-th rencontres number with the parameter $r$ is the number of permutations having exactly $r$ fixed points. In particular, a derangement is a permutation without any fixed point. We presents a short combinatorial proof for a weighted sum deran
Externí odkaz:
http://arxiv.org/abs/1711.04537
We prove that the difference between the $n$-th hyperfibonacci number of $r$-th generation and its two consecutive predecessors is the $n$-th regular $(r-1)$-topic number. Using this fact we provide an equivalent recursive definition of hyperfibonacc
Externí odkaz:
http://arxiv.org/abs/1606.06228
Autor:
Martinjak, Ivica, Urbiha, Igor
In this paper we extend a notion of Cassini determinant to recently introduced hyperfibonacci sequences. We find $Q$-matrix for the $r$-th generation hyperfibonacci numbers and prove an explicit expression of the Cassini determinant for these sequenc
Externí odkaz:
http://arxiv.org/abs/1509.03226
Autor:
Martinjak, Ivica
By means of associated structural invariants, we efficiently construct four biplanes of order 9 - except the one with the smallest automorphism group, that is found by Janko and Trung. The notion of non-transversal vector is introduced since we obser
Externí odkaz:
http://arxiv.org/abs/1509.03218
Autor:
Martinjak, Ivica, Vrsaljko, Iva
In this paper we extend the notion of Melham sum to the Pell and Pell-Lucas sequences. While the proofs of general statements rely on the binomial theorem, we prove some spacial cases by the known Pell identities. We also give extensions of obtained
Externí odkaz:
http://arxiv.org/abs/1508.04953
Autor:
Martinjak, Ivica, Prodinger, Helmut
In this paper we present two families of Fibonacci-Lucas identities, with the Sury's identity being the best known representative of one of the families. While these results can be proved by means of the basic identity relating Fibonacci and Lucas se
Externí odkaz:
http://arxiv.org/abs/1508.04949
Autor:
Martinjak, Ivica
In this paper we present a family of identities for recursive sequences arising from a second order recurrence relation, that gives instances of Zeckendorf representation. We prove these results using a special case of an universal property of the re
Externí odkaz:
http://arxiv.org/abs/1508.02762
Autor:
Martinjak, Ivica
In this note we prove two extensions of the Sury's identity.
Comment: 2 pages
Comment: 2 pages
Externí odkaz:
http://arxiv.org/abs/1508.01444