THE CHARNEY-DAVIS QUANTITY FOR CERTAIN GRADED POSETS
... subfamilies of posets of two kinds: disjoint unions of chains (Section 2), and products of two chains (Section 3). We should remark that there has been recent interest in the quantity analogous to W (P, −1) obtained by replacing the descent number des(w) with the major index maj(w) or the inversion ...
... subfamilies of posets of two kinds: disjoint unions of chains (Section 2), and products of two chains (Section 3). We should remark that there has been recent interest in the quantity analogous to W (P, −1) obtained by replacing the descent number des(w) with the major index maj(w) or the inversion ...
On a conjecture of Chowla and Milnor
... It is now known, thanks to the works of Goncharov [5] and Terasoma [13], that dk ≤ δk . The only known cases of Zagier’s conjecture are d2 = d3 = d4 = 1. Thus we do not have a single example where the dimension of Wk is at least 2. In this connection, we prove the following result. Theorem 3 The Cho ...
... It is now known, thanks to the works of Goncharov [5] and Terasoma [13], that dk ≤ δk . The only known cases of Zagier’s conjecture are d2 = d3 = d4 = 1. Thus we do not have a single example where the dimension of Wk is at least 2. In this connection, we prove the following result. Theorem 3 The Cho ...
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... Theorem 1: (Brison) Let p ≥ 5 be a prime number. A Φ2 -sequence (an )n is a complete Fibonacci sequence if and only if an = bn for all n, where b is a Fibonacci primitive root. The new results of this paper concern the case κ = 3. Because of the specific recurrence satisfied by Φ3 -sequences (an+3 = ...
... Theorem 1: (Brison) Let p ≥ 5 be a prime number. A Φ2 -sequence (an )n is a complete Fibonacci sequence if and only if an = bn for all n, where b is a Fibonacci primitive root. The new results of this paper concern the case κ = 3. Because of the specific recurrence satisfied by Φ3 -sequences (an+3 = ...
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... There are other kinds of promenades, practiced by mathematicians, stepping on numbers, in search of “flowers”; that is, numbers with especially interesting properties. There are many ways of walking on numbers, for example stepping on every number, one after the other; although one finds all the bea ...
... There are other kinds of promenades, practiced by mathematicians, stepping on numbers, in search of “flowers”; that is, numbers with especially interesting properties. There are many ways of walking on numbers, for example stepping on every number, one after the other; although one finds all the bea ...
Section 1.2-1.3
... Assume that ¬P (n) holds for some integer n b. Let N b be the least such integer satisfying ¬P (N ). Derive “a contradiction.” Definition 1.2.2. A natural number p > 1 is a prime number if and only if for all natural numbers a and b, if p = ab then either a = 1 or b = 1. When a natural number n > 1 ...
... Assume that ¬P (n) holds for some integer n b. Let N b be the least such integer satisfying ¬P (N ). Derive “a contradiction.” Definition 1.2.2. A natural number p > 1 is a prime number if and only if for all natural numbers a and b, if p = ab then either a = 1 or b = 1. When a natural number n > 1 ...
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... 109 and 777 has exactly n distinct prime divisors. From Fact 2 in [3], M1 is empty and, from the searches described in Sections 3 and 5, M2 and M3 have 330 and 9 elements, respectively. Since 2 • 3 • 5 • 7 • 11 • 13 • 17 • 19 • 23 • 29 > 10 9 , we see that Mn is empty if n > 9. If n = 8 or 9, then, ...
... 109 and 777 has exactly n distinct prime divisors. From Fact 2 in [3], M1 is empty and, from the searches described in Sections 3 and 5, M2 and M3 have 330 and 9 elements, respectively. Since 2 • 3 • 5 • 7 • 11 • 13 • 17 • 19 • 23 • 29 > 10 9 , we see that Mn is empty if n > 9. If n = 8 or 9, then, ...
An-introduction-to-Rational
... rational number terminating decimal mixed number repeating decimal bar notation ...
... rational number terminating decimal mixed number repeating decimal bar notation ...
JSUNIL TUTORIAL, SAMASTIPUR ...
... The rational number 0 is the additive identity for rational numbers. The rational number 1 is the multiplicative identity for rational numbers. ...
... The rational number 0 is the additive identity for rational numbers. The rational number 1 is the multiplicative identity for rational numbers. ...
Terminology of Algebra
... • It may seem that rational numbers would fill up all the gaps between integers on a number line, but they don’t • The next set of numbers to be considered will fill in the rest of the gaps between the integers and rational numbers on a number line • Irrational numbers – Numbers that can not be writ ...
... • It may seem that rational numbers would fill up all the gaps between integers on a number line, but they don’t • The next set of numbers to be considered will fill in the rest of the gaps between the integers and rational numbers on a number line • Irrational numbers – Numbers that can not be writ ...
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... Zeckendorf representations and arrays exist, for these sequences, as above. That is, the initial row of the array is the sequence ai,j = uj suitable shifted so the first two elements are 1 and an integer larger than 1. Subsequent rows begin with the smallest number that has not yet appeared, with th ...
... Zeckendorf representations and arrays exist, for these sequences, as above. That is, the initial row of the array is the sequence ai,j = uj suitable shifted so the first two elements are 1 and an integer larger than 1. Subsequent rows begin with the smallest number that has not yet appeared, with th ...
