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Polynomial identities from weighted lattice path counting

✍ Scribed by Şerban N. Buzeţeanu; Virgil Domocoş

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 154 KB
Volume: 150
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00209-f

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✦ Synopsis

We give bijective proofs, using weighted lattice paths, of two multinomial identities concerning the generalized h-factorial polynomials of order n.

[x]~, :=

The first-one is the multinomial identity of order s verified by these polynomials. Using this identity (and its proof) as a lemma, we derive the main identity that generalizes previous results of Carlitz (1977 and the classical identity of Banach.

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Counting pairs of nonintersecting lattic

Counting pairs of nonintersecting lattice paths with respect to weighted turns

✍ Christian Krattenthaler; Robert A. Sulanke 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 411 KB

A formula involving a difference of the products of four q-binomial coefficiems is shown to count pairs of nonintersecting lattice paths having a prescribed number of weighted turns. The weights are assigned to account for the location of the turns according to the major and lesser indices. The resu