What are some examples of allusion in the story, "The Necklace?"

It would be hard to find examples of specific allusions in "The Necklace" but there are examples of general allusions in Mathilde Loisel's fantasies and daydreams.

She thought of silent antechambers hung with Oriental tapestry, illumined by tall bronze candelabra, and of two great footmen in knee breeches who sleep in the big armchairs, made drowsy by the oppressive heat of the stove. She thought of long reception halls hung with ancient silk, of the...

It would be hard to find examples of specific allusions in "The Necklace" but there are examples of general allusions in Mathilde Loisel's fantasies and daydreams.

She thought of silent antechambers hung with Oriental tapestry, illumined by tall bronze candelabra, and of two great footmen in knee breeches who sleep in the big armchairs, made drowsy by the oppressive heat of the stove. She thought of long reception halls hung with ancient silk, of the dainty cabinets containing priceless curiosities and of the little coquettish perfumed reception rooms made for chatting at five o'clock with intimate friends, with men famous and sought after, whom all women envy and whose attention they all desire.

Here the narrator is alluding to the kind of lifestyle Mathilde feels should be hers; though she has never actually experienced this degree of wealth and leisure (she was born into an upper-middle-class family), she has witnessed the luxuries her wealthy friends command—and this haunts her imagination. She has a little Breton girl to do all her housework, eats well, and leads a comfortable life, yet still she is unhappy. 

Mathilde Loisel makes her own life miserable with her longing for things she cannot have. There are a number of similarities between the life Mathilde longs for and the portraits of such a life that appeared in romantic literature at the time. Perhaps Maupassant's descriptions allude to the cheap romantic literature of his day, suggesting that unrealistic portraits ultimately prove unsatisfying and destructive. Maupassant was a realist. His writing is the exact opposite of the highly derivative romantic fantasy literature he perhaps alludes to satirically in the passage quoted above.