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pro vyhledávání: '"Mikić, Jovan"'
Autor:
Mikić, Jovan
We present a new formula for the highest power of $a+b$ that divides the sum $B(n,m,a,b)=\sum_{k=0}^{n}\binom{n}{k}^m a^{n-k}b^k$ for the case $m=2$. By using this formula, we give complete 3-adic valuation for central Dellanoy numbers. Also, we find
Externí odkaz:
http://arxiv.org/abs/2311.14623
Autor:
Mikić, Jovan
We consider a new class of matrices associated to a real square matrix $A$ and to a vector $\vec{c} \in \{-1,1\}^n$ such that $c_1=1$ by using a map $\varphi_{\vec{c}}$ which turns out to be a conjugation of a matrix $A$ by a signature matrix. It is
Externí odkaz:
http://arxiv.org/abs/2309.08933
Autor:
Mikić, Jovan
The Gessel number $P(n,r)$ is the number of the paths in plane with $(1, 0)$ and $(0,1)$ steps from $(0,0)$ to $(n+r, n+r-1)$ that never touch any of the points from the set $\{(x,x)\in \mathbb{Z}^2: x\geq r\}$. We show that there is a close relation
Externí odkaz:
http://arxiv.org/abs/2206.03808
Autor:
Mikić, Jovan
The Gessel number $P(n,r)$ represents the number of lattice paths in a plane with unit horizontal and vertical steps from $(0,0)$ to $(n+r,n+r-1)$ that never touch any of the points from the set $\{(x,x)\in \mathbb{Z}^2: x \geq r\}$. In this paper, w
Externí odkaz:
http://arxiv.org/abs/2203.12931
Autor:
Mikić, Jovan
Publikováno v:
Romanian Mathematical Magazine, 15 march 2021
We present a new alternating convolution formula for the super Catalan numbers which arises as a generalization of two known binomial identities. We prove a generalization of this formula by using auxiliary sums, recurrence relations, and induction.
Externí odkaz:
http://arxiv.org/abs/2110.04805