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 Bruhat–Tits Building In mathematics, a building (also Tits building, Bruhat–Tits building, named after François Bruhat and Jacques Tits) is a combinatorial and geometric structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes, and Riemannian symmetric spaces [...More...] "Bruhat–Tits Building" on: Wikipedia Google Yahoo Parouse picture info Mathematics Mathematics Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change. It has no generally accepted definition. Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist [...More...] "Mathematics" on: Wikipedia Google Yahoo Parouse Flag (linear Algebra) In mathematics, particularly in linear algebra, a flag is an increasing sequence of subspaces of a finite-dimensional vector space V. Here "increasing" means each is a proper subspace of the next (see filtration): 0 = V 0 ⊂ V 1 ⊂ V 2 ⊂ ⋯ ⊂ V k = V . displaystyle 0 =V_ 0 subset V_ 1 subset V_ 2 subset cdots subset V_ k =V. If we write the dim Vi = di then we have 0 = d 0 < d 1 < d 2 < ⋯ < d k = n , displaystyle 0=d_ 0