Zobrazeno 1 - 10
of 167
pro vyhledávání: '"05A10, 05A19"'
Autor:
Adegoke, Kunle
We give a short proof of the well-known Knuth's old sum and provide some generalizations. Our approach utilizes the binomial theorem and integration formulas derived using the Beta function. Several new polynomial identities and combinatorial identit
Externí odkaz:
http://arxiv.org/abs/2412.00040
Autor:
Sun, Zhi-Hong
Let $\{A'_n\}$ be the Ap\'ery numbers given by $A'_n=\sum_{k=0}^n\binom nk^2\binom{n+k}k.$ For any prime $p\equiv 3\pmod 4$ we show that $A'_{\frac{p-1}2}\equiv \frac{p^2}3\binom{\frac{p-3}2}{\frac{p-3}4}^{-2}\pmod {p^3}$. Let $\{t_n\}$ be given by $
Externí odkaz:
http://arxiv.org/abs/2409.06544
Autor:
Beauduin, Kei
In this paper, we explore the effectiveness of almost purely operational methods in the study of umbral calculus. To accomplish this goal, we systematically reconstruct the theory operationally, offering new proofs and results throughout. Our approac
Externí odkaz:
http://arxiv.org/abs/2407.16348
Autor:
Jang, Jihyeug, Song, Minho
Orthogonal polynomials on the unit circle (OPUC for short) are a family of polynomials whose orthogonality is given by integration over the unit circle in the complex plane. There are combinatorial studies on the moments of various types of orthogona
Externí odkaz:
http://arxiv.org/abs/2407.07508
Autor:
Amdeberhan, Tewodros, Tauraso, Roberto
One variant of the $q$-Catalan polynomials is defined in terms of Gaussian polynomials by $\mathcal{C}_k(q)=\genfrac{[}{]}{0pt}{}{2k}{k}_q-q\genfrac{[}{]}{0pt}{}{2k}{k+1}_q$. Liu studied congruences of the form $\sum_{k=0}^{n-1} q^k\mathcal{C}_k$ mod
Externí odkaz:
http://arxiv.org/abs/2406.12332
Autor:
Beauduin, Kei
Publikováno v:
Enumer. Comb. Appl. 5:1 (2025) Article S2R4
In this paper, we derive formal general formulas for noncommutative exponentiation and the exponential function, while also revisiting an unrecognized, and yet powerful theorem. These tools are subsequently applied to derive counterparts for the expo
Externí odkaz:
http://arxiv.org/abs/2405.03001
We study a multispecies $t$-PushTASEP system on a finite ring of $n$ sites with site-dependent rates $x_1,\dots,x_n$. Let $\lambda=(\lambda_1,\dots,\lambda_n)$ be a partition whose parts represent the species of the $n$ particles on the ring. We show
Externí odkaz:
http://arxiv.org/abs/2403.10485
We investigate the moment problem and Jacobi matrix associated -- by the operator theoretic framework of the semilocal trace formula -- to each finite set $S$ of places of $\mathbb Q$ containing the archimedean place. The measure is given by the abso
Externí odkaz:
http://arxiv.org/abs/2403.01247
We establish, for every family of orthogonal polynomials in the $q$-Askey scheme and the Askey scheme, a combinatorial model for mixed moments and coefficients in terms of paths on the lecture hall graph. This generalizes the previous results of Cort
Externí odkaz:
http://arxiv.org/abs/2311.12761
Autor:
Aicardi, Francesca
We show how the Fuss-Catalan numbers $ \frac{1}{p n+1}\binom{pn+1}{n}$ enter different problems of counting simple and multiple planar partitions.
Comment: 10 pages, 6 figures
Comment: 10 pages, 6 figures
Externí odkaz:
http://arxiv.org/abs/2311.02245