5 citations · 6 across the 8 of their papers we have counts for
14 papers
Weighted Lattice Paths Enumeration by Gaussian Polynomials
Ivica Martinjak, Ivana Zubac
The Gaussian polynomial in variable is defined as the -analog of the binomial coefficient. In addition to remarkable implications of these polynomials to abstract algebra, m…
Lah numbers and Lindström's lemma
Ivica Martinjak, Riste Škrekovski
We provide a combinatorial interpretation of Lah numbers by means of planar networks. Henceforth, as a conesquence of Lindström's lemma, we conclude that the related Lah matrix pos…
A Short Combinatorial Proof of Derangement Identity
Ivica Martinjak, Dajana Stanić
The -th rencontres number with the parameter is the number of permutations having exactly fixed points. In particular, a derangement is a permutation without any fixed p…
Hyperfibonacci Sequences and Polytopic Numbers
Ligia Loretta Cristea, Ivica Martinjak, Igor Urbiha
We prove that the difference between the -th hyperfibonacci number of -th generation and its two consecutive predecessors is the -th regular -topic number. Using th…
A New Generalized Cassini Determinant
Ivica Martinjak, Igor Urbiha
In this paper we extend a notion of Cassini determinant to recently introduced hyperfibonacci sequences. We find -matrix for the -th generation hyperfibonacci numbers and pro…
Non-transversal Vectors of Some Finite Geometries
Ivica Martinjak
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 Tr…
On Polynomial Identities for Recursive Sequences
Ivica Martinjak, Iva Vrsaljko
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 ca…
A Family of the Zeckendorf Theorem Related Identities
Ivica Martinjak
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…
Two Extensions of the Sury's Identity
Ivica Martinjak
In this note we prove two extensions of the Sury's identity.
Complementary Families of the Fibonacci-Lucas Relations
Ivica Martinjak, Helmut Prodinger
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…
Hadamard Structures with Associated Automorphisms
Ivica Martinjak
In this paper we present new Hadamard matrices and related combinatorial structures. In particular, it is constructed 5202 inequivalent Hadamard matrices of order 36 as well as 180…
Some Families of Identities for Integer Partition Function
Ivica Martinjak, Dragutin Svrtan
We give a series of recursive identities for the number of partitions with exactly parts and with constraints on both the minimal difference among the parts and the minimal par…
A class of symmetric association schemes as inclusion of biplanes
Ivica Martinjak
Let be a nontrivial biplane of order represented by symmetric canonical incidence matrix with trace . We proved that includes a partial…
New identities for the polarized partitions and partitions with -distant parts
Ivica Martinjak, Dragutin Svrtan
In this paper we present a new class of integer partition identities. The number of partitions with d-distant parts can be represented as a sum of the number of partitions with 1-d…