منابع مشابه
Dedicated to John Riordan on the Occasion of His 75th Birthday
Baxter permutations apparently first arose in attempts to prove the “commuting function” conjecture of Dyer (see [I]), namely, if f and g are continuous functions mapping [0, l] into [0, l] which commute under composition, then they have a common fixed point. Although numerous partial results were obtained for the conjecture (e.g., see [l, 3, 7, IO]), it was ultimately shown in 1967 to be false...
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Riordan paths are Motzkin paths without horizontal steps on the x-axis. We establish a correspondence between Riordan paths and (321, 31̄42)-avoiding derangements. We also present a combinatorial proof of a recurrence relation for the Riordan numbers in the spirit of the Foata-Zeilberger proof of a recurrence relation on the Schröder numbers.
متن کاملGeneralized Riordan arrays
In this paper, we generalize the concept of Riordan array. A generalized Riordan array with respect to cn is an infinite, lower triangular array determined by the pair (g(t), f(t)) and has the generic element dn,k = [t/cn]g(t)(f(t))/ck, where cn is a fixed sequence of non-zero constants with c0 = 1. We demonstrate that the generalized Riordan arrays have similar properties to those of the class...
متن کاملSemiorders and Riordan Numbers
In this paper, we define a class of semiorders (or unit interval orders) that arose in the context of polyhedral combinatorics. In the first section of the paper, we will present a pure counting argument equating the number of these interesting (connected and irredundant) semiorders on n + 1 elements with the nth Riordan number. In the second section, we will make explicit the relationship betw...
متن کاملComplementary Riordan arrays
Recently, the concept of the complementary array of a Riordan array (or recursive matrix) has been introduced. Here we generalize the concept and distinguish between dual and complementary arrays. We show a number of properties of these arrays, how they are computed and their relation with inversion. Finally, we use them to find explicit formulas for the elements of many recursive matrices.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1978
ISSN: 0097-3165
DOI: 10.1016/0097-3165(78)90055-9