The hypergeometric functions nFn−1 are higher transcendental functions, but for certain parameter values they become algebraic. This occurs, e.g., if the defining hypergeometric differential equation has irreducible but imprimitive monodromy. It is shown that many algebraic nFn−1’s of this type can be represented as combinations of certain explicitly algebraic functions of a single variable, i....

in public ceremonies, some of the deepest collective memories of the city are being shaped. in safavid era, feasts and funerals; which were either celebration of iranian old traditions or shiite rituals, provided some of the most memorable scenes in public life of the city. this has been mentioned frequently in itineraries and travelogues - both iranians and foreigners. these ceremonies gradual...

A character identity which relates irreducible values of the hyperoctahedral group \(B_n\) to those symmetric \(S_{2n}\) was recently proved by Lübeck and Prasad. Their proof is algebraic involves Lie theory. We present a short combinatorial this identity, as well generalization other wreath products.Mathematics Subject Classifications: 20C30, 20E22, 05E10Keywords: Character product, partition,...

in this paper, let $l$ be a completeresiduated lattice, and let {bf set} denote the category of setsand mappings, $lf$-{bf pos} denote the category of $lf$-posets and$lf$-monotone mappings, and $lf$-{bf cslat}$(sqcup)$, $lf$-{bfcslat}$(sqcap)$ denote the category of $lf$-completelattices and $lf$-join-preserving mappings and the category of$lf$-complete lattices and $lf$-meet-preserving mapping...

The Fundamental Lemma is a somewhat obscure combinatorial identity introduced by Robert P. Langlands in 1979 as an ingredient in the theory of automorphic representations. After many years of deep contributions by mathematicians working in representation theory, number theory, algebraic geometry, and algebraic topology, a proof of the Fundamental Lemma was recently completed by Ngô Bao Châu in ...