Zobrazeno 1 - 10
of 446
pro vyhledávání: '"SOKAL, ALAN"'
We introduce some classes of increasing labeled and multilabeled trees, and we show that these trees provide combinatorial interpretations for certain Thron-type continued fractions with coefficients that are quasi-affine of period 2. Our proofs are
Externí odkaz:
http://arxiv.org/abs/2412.10214
Autor:
Sokal, Alan D., Walrad, James
We give a continued-fraction characterization of Stieltjes moment sequences for which there exists a representing measure with support in $[\xi, \infty)$. The proof is elementary.
Comment: LaTeX2e, 10 pages. arXiv admin note: text overlap with a
Comment: LaTeX2e, 10 pages. arXiv admin note: text overlap with a
Externí odkaz:
http://arxiv.org/abs/2404.12131
We introduce a triangular array $\widehat{\sf L}^{(\alpha)}$ of 5-variable homogeneous polynomials that enumerate Laguerre digraphs (digraphs in which each vertex has out-degree 0 or 1 and in-degree 0 or 1) with separate weights for peaks, valleys, d
Externí odkaz:
http://arxiv.org/abs/2312.11081
Autor:
Deb, Bishal, Sokal, Alan D.
We prove the coefficientwise Hankel-total positivity of the even and odd subsequences of Schett polynomials $X_n(x,y,z)$.
Comment: LaTeX2e, 12 pages, extended abstract submitted to FPSAC 2024
Comment: LaTeX2e, 12 pages, extended abstract submitted to FPSAC 2024
Externí odkaz:
http://arxiv.org/abs/2311.11747
Autor:
Deb, Bishal, Sokal, Alan D.
Publikováno v:
Electronic Journal of Combinatorics 31(2), #P2.14 (2024)
We show that very simple continued fractions can be obtained for the ordinary generating functions enumerating permutations or D-permutations with a large number of independent statistics, when each cycle is given a weight $-1$. The proof is based on
Externí odkaz:
http://arxiv.org/abs/2306.11500
Autor:
Deb, Bishal, Sokal, Alan D.
Publikováno v:
Ramanujan J. 65, 1013-1060 (2024)
A permutation is said to be cycle-alternating if it has no cycle double rises, cycle double falls or fixed points; thus each index $i$ is either a cycle valley ($\sigma^{-1}(i)>i<\sigma(i)$) or a cycle peak ($\sigma^{-1}(i)\sigma(i)$). We find Stielt
Externí odkaz:
http://arxiv.org/abs/2304.06545
Autor:
Chen, Xi, Sokal, Alan D.
Publikováno v:
Adv. Appl. Math. 157, 102703 (2024)
We study three combinatorial models for the lower-triangular matrix with entries $t_{n,k} = \binom{n}{k} n^{n-k}$: two involving rooted trees on the vertex set $[n+1]$, and one involving partial functional digraphs on the vertex set $[n]$. We show th
Externí odkaz:
http://arxiv.org/abs/2302.03999
Autor:
Deb, Bishal, Sokal, Alan D.
A D-permutation is a permutation of $[2n]$ satisfying $2k-1 \le \sigma(2k-1)$ and $2k \ge \sigma(2k)$ for all $k$; they provide a combinatorial model for the Genocchi and median Genocchi numbers. We find Stieltjes-type and Thron-type continued fracti
Externí odkaz:
http://arxiv.org/abs/2212.07232
Autor:
Sokal, Alan D.
Publikováno v:
Expositiones Mathematicae 41, 245--287 (2023)
I present and discuss an extremely simple algorithm for expanding a formal power series as a continued fraction. This algorithm, which goes back to Euler (1746) and Viscovatov (1805), deserves to be better known. I also discuss the connection of this
Externí odkaz:
http://arxiv.org/abs/2206.15434