Towards computerized proofs of identities
نویسندگان
چکیده
منابع مشابه
Towards Computerized Proofs of Identities
Many of the seemingly trivial facts that we take for granted are really theorems, like the fact that 11 x 12 = 132, or that \ + \ = | . The reason that these are no longer thought of as theorems is that nowadays quite routine algorithms perform these tasks. The same is true, thanks to modern computer algebra programs, for 20 20 the "theorem" that (a + b) —a H , or, thanks to the recent completi...
متن کاملAutomatic Proofs of Identities
We present the ideas behind algorithmic proofs of identities involving sums and integrals of large classes of special functions. Recent results allowed a new extension of the class of holonomic functions.
متن کاملAbacus Proofs of Schur Function Identities
This article uses combinatorial objects called labeled abaci to give direct combinatorial proofs of many familiar facts about Schur polynomials. We use abaci to prove the Pieri rules, the Littlewood–Richardson rule, the equivalence of the tableau definition and the determinant definition of Schur polynomials, and the combinatorial interpretation of the inverse Kostka matrix (first given by Eğec...
متن کاملCombinatorial Proofs of Identities Involving Symmetric Matrices
Brualdi and Ma found a connection between involutions of length n with k descents and symmetric k×k matrices with non-negative integer entries summing to n and having no row or column of zeros. From their main theorem they derived two alternating sums by algebraic means and asked for combinatorial proofs. The purpose of this note is to give such demonstrations.
متن کاملBijective proofs of Gould's and Rothe's identities
We first give a bijective proof of Gould’s identity in the model of binary words. Then we deduce Rothe’s identity from Gould’s identity again by a bijection, which also leads to a double-sum extension of the q-Chu-Vandermonde formula.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1990
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1990-15904-x