37(2)
... In the previous section, we showed that F(x) generates only even balancing numbers, whereas K(x) generates only odd balancing numbers. But H(x) and K(x) generate both even and odd balancing numbers. Since H(6) = 204 and there is a balancing number 35 between 6 and 204, it is clear that H(x) does not ...
... In the previous section, we showed that F(x) generates only even balancing numbers, whereas K(x) generates only odd balancing numbers. But H(x) and K(x) generate both even and odd balancing numbers. Since H(6) = 204 and there is a balancing number 35 between 6 and 204, it is clear that H(x) does not ...
SET PARTITION ASYMPTOTICS AND A CONJECTURE OF GOULD
... set. The Bn are known as the Bell numbers. Their sequence starts with 1, 1, 2, 5, 15, 52, 203, 877, · · · for n = 0, 1, 2, · · · (see [8, Section 1.4], A000110 in [1]). It is a fact (see [7]) that the canonical representations of all set partitions of [n] are precisely the words π = π1 π2 · · · πn s ...
... set. The Bn are known as the Bell numbers. Their sequence starts with 1, 1, 2, 5, 15, 52, 203, 877, · · · for n = 0, 1, 2, · · · (see [8, Section 1.4], A000110 in [1]). It is a fact (see [7]) that the canonical representations of all set partitions of [n] are precisely the words π = π1 π2 · · · πn s ...
CONNECTED COVERING NUMBERS 1. Introduction Let n, k, r be
... Let us now show that D is connected. Clearly, all blocks in a given Ai are connected and all 2-element subsets in each Ai are covered by a block in this Ai . Thus, it suffices to verify that there are two 2-element sets {e, f } ⊆ A0 and {e0 , f 0 } ⊆ A2 which can be connected by a sequence of blocks ...
... Let us now show that D is connected. Clearly, all blocks in a given Ai are connected and all 2-element subsets in each Ai are covered by a block in this Ai . Thus, it suffices to verify that there are two 2-element sets {e, f } ⊆ A0 and {e0 , f 0 } ⊆ A2 which can be connected by a sequence of blocks ...
