Results

**1 - 4**of**4**### Table 1: The summary of previous and our results.

2004

"... In PAGE 2: ... Finally, on SODA 1995 Gaber and Mansour have published an upper bound of O(Rad + log5 n), which is the state-of-the-art. See Table1 for the summary of previous and our results.... ..."

### Table 1 Summary of known lower and upper bounds on convergence complexity for optimistic, bottleneck rate-based flow control algorithms.

1997

"... In PAGE 36: ... A more complete presentation of results for the model studied in this paper (and extensions of it) can be found in [8]. For the sake of completeness and comparison, we summarize in Table1 all known lower and upper bounds on the convergence complexity of optimistic, bottleneck algo- rithms for rate-based flow control, established in this work and in the preceding work by Afek, Mansour, and Ostfeld [1]. We remark that RoundRobin represents an expo- nential improvement over the previous algorithm Arbitrary [1, section 6] for the class of oblivious algorithms we introduced.... ..."

Cited by 3

### Table 11. Avoidance of generalized patterns in permutations

"... In PAGE 19: ... Relations to several well studied combinatorial structures, such as set partitions (see [105]), Dyck paths (see [163]), Motzkin paths (see [66]) and involutions (see [200]), were shown there. The main results from that paper are given in Table11 , where Bn is the n-th Bell number, Cn is the n-th Catalan number, and Bstar n is the n-th Bessel number. For some other results on generalized permutation patterns see [63, 64, 113, 114, 115, 117, 118, 142, 146, 147].... In PAGE 19: ...Table 11. Avoidance of generalized patterns in permutations As in the paper by Simion and Schmidt [199], dealing with the classical patterns, Claes- son [62], Claesson and Mansour [63] considered a number of cases when permutations have to avoid two or more generalized patterns simultaneously (see Table11 ). In [113], Kitaev gave either an explicit formula or a recursive formula for almost all cases of simul- taneous avoidance of more than two generalized patterns of length three with no dashes, and listed what was known about double restrictions (the remaining cases were described... ..."

Cited by 2

### Table 1. Examples of symmetry classes

"... In PAGE 19: ... Relations to several well studied combinatorial structures, such as set partitions (see [105]), Dyck paths (see [163]), Motzkin paths (see [66]) and involutions (see [200]), were shown there. The main results from that paper are given in Table1 1, where Bn is the n-th Bell number, Cn is the n-th Catalan number, and Bstar n is the n-th Bessel number. For some other results on generalized permutation patterns see [63, 64, 113, 114, 115, 117, 118, 142, 146, 147].... In PAGE 19: ... patterns P |Sn(P )| description 1-23 Bn partitions of [n] 1-32 Bn partitions of [n] 2-13 Cn Dyck paths of length 2n 1-23, 12-3 Bstar n non-overlapping partitions of [n] 1-23, 1-32 In involutions in Sn 1-23, 13-2 Mn Motzkin paths of length n Table 11. Avoidance of generalized patterns in permutations As in the paper by Simion and Schmidt [199], dealing with the classical patterns, Claes- son [62], Claesson and Mansour [63] considered a number of cases when permutations have to avoid two or more generalized patterns simultaneously (see Table1 1). In [113], Kitaev gave either an explicit formula or a recursive formula for almost all cases of simul- taneous avoidance of more than two generalized patterns of length three with no dashes, and listed what was known about double restrictions (the remaining cases were described... ..."

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