Now showing items 1-10 of 75
A Wilf class composed of 19 symmetry classes of quadruples of 4-letter patterns
(Bulgarian Acad Science, 2017)
In this paper, we make a contribution to the enumeration of permutations avoiding a quadruples of 4-letter patterns by establishing a Wilf class composed of 19 symmetry classes.
Evaluation of Hessenberg Determinants via Generating Function Approach
(University of Nis, 2017)
In this paper, we will present various results on computing of wide classes of Hessenberg matrices whose entries are the terms of any sequence. We present many new results on the subject as well as our results will cover ...
Formulæ related to the q-Dixon formula with applications to Fibonomial sums
(Kluwer Academic Publishers, 2015-06)
The -analogue of Dixon's identity involves three -binomial coefficients as summands. We find many variations of it that have beautiful corollories in terms of Fibonomial sums. Proofs involve either several instances of the ...
Closed form evaluation of restricted sums containing squares of Fibonomial coefficients
(Politechnica University of Bucharest, 2016)
We give a systematic approach to compute certain sums of squares Fibonomial coefficients with powers of generalized Fibonacci and Lucas numbers as coefficients; the range of the summation is not the natural one but about ...
Ruehr's identities with two additional parameters
We present generalizations of Ruehr’s identities with two additional parameters. We prove the claimed results by two di?erent proof methods, namely combinatorially and mechanically. Further, we derive recurrence relations ...
Evaluation of sums involving Gaussian q-binomial coefficients with rational weight functions
(World Scientific Publishing Co. Pte Ltd, 2016-03)
We consider sums of the Gaussian q-binomial coefficients with a parametric rational weight function. We use the partial fraction decomposition technique to prove the claimed results. We also give some interesting applications ...
Sylvester-Tridiagonal Matrix with Alternating main diagonal entries and its Spectra
(Walter De Gruyter Gmbh, 2013-11)
Recently some generalizations of Sylvester type tridiagonal matrices have been considered with their spectra. We introduce a new kind generalization of Sylvester type tridiagonal matrix by considering its main diagonal entries. ...
On Alternating Weighted Binomıal Sums With Falling Factorıals
(Int Center Scientific Research & Studies, 2017)
In this paper, by inspiring from earlier recent works on weighted binomial sums, we introduce and compute new kinds of binomial sums including rising factorial of the summation indices.
A class of non-symmetric band determinants with the Gaussian q-binomialcoefficients
(Taylor and Francis Ltd., 2017)
A class of symmetric band matrices of bandwidth 2r+1 with the binomial coefficients entries was studied earlier. We consider a class of non-symmetric band matrices with the Gaussian q-binomial coefficients whose upper ...
The generalized Lilbert matrix
We introduce a generalized Lilbert [Lucas-Hilbert] matrix. Explicit formul' are derived for the LU-decomposition and their inverses, as well as the Cholesky decomposition. The approach is to use q-analysis and to leave the ...