6 citations · 6 across the 12 of their papers we have counts for
19 papers
Graph binomial coefficients and a positivity conjecture of Guo and Krattenthaler
Madjid Mirzavaziri, Daniel Yaqubi
We investigate Conjecture 7.4 of Guo and Krattenthaler \cite{GK}, which predicts that for every positive integer , the polynomial \[ P_n(q) = \frac{(1-q)^2}{(1-q^{10n-1})(1-q^{1…
Riordan Arrays and Shifted Hankel Determinants of OEIS A005773
Daniel Yaqubi, Madjid Mirzavaziri
We study two Riordan arrays associated with the Motzkin-prefix sequence (\href{https://oeis.org/A005773}{OEIS A005773}). By connecting their production matrices through a simple bo…
Cyclic Latin Eulerian Numbers
Madjid Mirzavaziri, Daniel Yaqubi
We introduce the directed cyclic difference inventory to study Latin Eulerian numbers restricted to row-reorderings of the cyclic Latin square, offering an orient…
Latin Eulerian Numbers
Madjid Mirzavaziri, Daniel Yaqubi
We introduce \emph{Latin Eulerian numbers} $\LE{n\atop k_1,\dots,k_n}$, a multivariate refinement of classical Eulerian numbers counting order- Latin squares by column ascents.…
A Combinatorial Problem in Cinema Seating
Madjid Mirzavaziri, Daniel Yaqubi
We address a problem concerning cinema audiences: ``A cinema has seats numbered from to , and there are people with tickets numbered from to . People enter th…
Prime and Touchard Congruences of Mixed-Type Bell Numbers
Daniel Yaqubi, Madjid Mirzavaziri
This paper establishes a comprehensive combinatorial and arithmetic framework for mixed Stirling and mixed Bell numbers, bridging partition structures, Touchard polynomials, and pr…
Arithmetic Properties of Mixed Stirling Numbers of the second kind
Daniel Yaqubi, Madjid Mirzavaziri
We investigate the mixed Stirling numbers of the second kind, , which count partitions of distinct elements into unlabeled and labeled non-e…
On the Graphical -Stirling Numbers of the First Kind for Specific Graph Families
Daniel Yaqubi, Madjid Mirzavaziri
This paper investigates the \textbf{graphical -Stirling numbers of the first kind}, denoted by $\str{G}{k}$, which enumerate partitions of a vertex set into disjoint…
Some properties of Zumkeller numbers and -layered numbers
Pankaj Jyoti Mahanta, Manjil P. Saikia, Daniel Yaqubi
Generalizing the concept of a perfect number is a Zumkeller or integer perfect number that was introduced by Zumkeller in 2003. The positive integer is a Zumkeller number if it…
Some results on average of Fibonacci and Lucas sequences
Daniel Yaqubi, Amirali Fatehizadeh
In this paper, we discuss about some results on average of Fibonacci and Lucas sequences that may be found in the OEIS code A111035.
Mixed coloured permutations
Beáta Bényi, Daniel Yaqubi
In this paper we introduce mixed coloured permutation, permutations with certain coloured cycles, and study the enumerative properties of these combinatorial objects. We derive the…
Mixed restricted Stirling numbers
Somaya Barati, Beáta Bényi, Abbas Jafarzadeh +1
In this note we investigate mixed partitions with extra condition on the sizes of the blocks. We give a general formula and the generating function. We consider in more details a s…
Some determinants of path generating functions, II
Christian Krattenthaler, Daniel Yaqubi
We evaluate Hankel determinants of matrices in which the entries are generating functions for paths consisting of up-steps, down-steps and level steps with a fixed starting point b…
Lattice paths inside a table, II
Daniel Yaqubi, Mohammad Farrokhi Derakhshandeh Ghouchan, Mohamad Zamani khademanlu
Consider an table and latices paths in such that each step , or . The number of paths from the -blank…
Some divisibility properties of binomial coefficients
Daniel Yaqubi, Madjid Mirzavaziri
In this paper, we gave some properties of binomial coefficient.
Spanning k-ended trees of 3-regular connected graphs
Hamed Ghasemian Zoeram, Daniel Yaqubi
A tree is called k-ended tree if it has at most k leaves, where a leaf is a vertex of degree one. In this paper we prove that every 3-regular connected graph with n vertices such t…
The Twelvefold way, the non-intersecting circles problem, and partitions of multisets
Toufik Mansour, Madjid Mirzavaziri, Daniel Yaqubi
Let be a non-negative integer and be a multi-set with not necessarily distinct members, where . We denote by $Δ(n,A)…
Mixed r-stirling numbers of the second kind
Daniel Yaqubi, Madjid Mirzavaziri, Yasin Saeednezhad
The Stirling number of the second kind counts the number of ways to partition a set of labeled balls into non-empty unlabeled cells. As an extension of this, we…
Some results on ordered and unordered factorization of a positive integers
Daniel Yaqubi, Madjid Mirzavaziri
As a well-known enumerative problem, the number of solutions of the equation with in positive integers is $Π(m,k)=\sum_{i=0}^kΠ(m-k,i…