Formal proofs of degree 5 binary BBP-type formulas

A Compendium of BBP-Type Formulas for Mathemati al Constants

Combinatorial Proofs of Addition Formulas

In this paper we give a combinatorial proof of an addition formula for weighted partial Motzkin paths. The addition formula allows us to determine the LDU decomposition of a Hankel matrix of the polynomial sequence defined by weighted partial Motzkin paths. As a direct consequence, we get the determinant of the Hankel matrix of certain combinatorial sequences. In addition, we obtain an addition...

Finite Proofs for Infinitary Formulas

Recent work has shown that the infinitary logic of hereand-there is closely related to the input language of the ASP grounder gringo. A formal system axiomatizing that logic exists, but a proof in that system may include infinitely many formulas. In this note, we define a correspondence between the validity of infinitary formulas in the logic of here-and-there and the provability of formulas in...

Algebraic Proofs over Noncommutative Formulas

We study possible formulations of algebraic propositional proof systems operating with noncommutative formulas. We observe that a simple formulation gives rise to systems at least as strong as Frege, yielding a semantic way to define a Cook-Reckhow (i.e., polynomially verifiable) algebraic analog of Frege proofs, different from that given in Buss et al. (1997) and Grigoriev & Hirsch (2003). We ...

2 01 5 Tokuyama - Type Formulas for Type B

Abstract. We obtain explicit formulas for the product of a deformed Weyl denominator with the character of an irreducible representation of the spin group Spin2r+1(C), which is an analogue of the formulas of Tokuyama for Schur polynomials and Hamel-King for characters of symplectic groups. To give these, we start with a symplectic group and obtain such characters using the Casselman-Shalika for...